Improving Lateral Flow Assay Performance Using Computational Modeling

Article (PDF Available)inAnnual Review of Analytical Chemistry (2008) 11(1) · June 2018with 611 Reads
DOI: 10.1146/annurev-anchem-061417-125737
Abstract
The performance, field utility, and low cost of lateral flow assays (LFAs) have driven a tremendous shift in global health care practices by enabling diagnostic testing in previously unserved settings. This success has motivated the continued improvement of LFAs through increasingly sophisticated materials and reagents. However, our mechanistic understanding of the underlying processes that drive the informed design of these systems has not received commensurate attention. Here, we review the principles underpinning LFAs and the historical evolution of theory to predict their performance. As this theory is integrated into computational models and becomes testable, the criteria for quantifying performance and validating predictive power are critical. The integration of computational design with LFA development offers a promising and coherent framework to choose from an increasing number of novel materials, techniques, and reagents to deliver the low-cost, high-fidelity assays of the future. Expected final online publication date for the Annual Review of Analytical Chemistry Volume 11 is June 12, 2018. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Annual Review of Analytical Chemistry
Improving Lateral Flow
Assay Performance Using
Computational Modeling
David Gasperino,1Ted Baughman,1Helen V. Hsieh,1
David Bell,1and Bernhard H. Weigl1,2
1Intellectual Ventures Laboratory, Bellevue, Washington 98007, USA
2Department of Bioengineering, University of Washington, Seattle, Washington 98195, USA
Annu. Rev. Anal. Chem. 2018. 11:23.1–23.26
The Annual Review of Analytical Chemistry is online
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061417-125737
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2018 by Annual Reviews.
All rights reserved
Keywords
lateral flow assay, computational modeling, optimization, reaction theory,
transport theory
Abstract
The performance, field utility, and low cost of lateral flow assays (LFAs) have
driven a tremendous shift in global health care practices by enabling diag-
nostic testing in previously unserved settings. This success has motivated the
continued improvement of LFAs through increasingly sophisticated materi-
als and reagents. However, our mechanistic understanding of the underlying
processes that drive the informed design of these systems has not received
commensurate attention. Here, we review the principles underpinning LFAs
and the historical evolution of theory to predict their performance. As this
theory is integrated into computational models and becomes testable, the
criteria for quantifying performance and validating predictive power are
critical. The integration of computational design with LFA development
offers a promising and coherent framework to choose from an increasing
number of novel materials, techniques, and reagents to deliver the low-cost,
high-fidelity assays of the future.
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1. INTRODUCTION
Lateral flow assays (LFAs), also known as rapid diagnostic tests (RDTs) and immunochromato-
graphic assays, are easy to use, low cost, and rapid; they also require little or no equipment to
operate and do not need to be refrigerated. Perhaps most importantly, they are very easy to pro-
duce, and more than 2 billion LFAs are manufactured each year, including over 400 million/year
each for malaria and HIV tests (1).
However, LFAs are generally not considered to be very sensitive. This perception is not due
to a fundamental property of LFAs but is rather a consequence of the way they are developed,
manufactured, and marketed. Even the highest-volume markets for LFAs generate relatively little
revenue compared to other diagnostics products, largely because of their low cost, primary use in
low-resource settings, and/or bulk procurement by donor-funded programs. Thus, most lateral
flow tests are developed and optimized by relatively small-scale manufacturers with limited re-
search and development capabilities and budgets and are generally used only for easily measured
analytical targets that present at high concentrations. Global Good, a collaboration between In-
tellectual Ventures and Bill Gates to develop technologies for humanitarian impact, is developing
LFA-based tests for use in global health applications that are as sensitive as the best conventional
point-of-care (POC) diagnostic assays (in some cases even better) while retaining all of their cost,
simplicity, and usability advantages.
In the most basic form (Figure 1), LFAs are characterized by a conjugate comprising a signal
particle and a binding molecule dried down on a porous pad that is placed on top of a membrane. A
few drops of sample containing the analyte are placed on top or in front of the conjugate, with the
analyte reacting with the conjugate as the resulting complex flows laterally along the membrane.
A capture line comprising a second binding reagent to the analyte then captures the complex,
resulting in a visible line.
Key elements that make the LFA process effective are appropriately timing the reactions be-
tween the binding reagents and the analyte while minimizing nonspecific binding of analyte,
a
b
c
d
Gold particle
with antibodies
Test zone Control
zone
Absorbent
pad
Conjugate
pad
Protein
analyte
Sample +
Analytical membrane
Sample pad
Figure 1
Schematic describing the location of reagents and porous membranes in a typical lateral flow assay (a) prior to sample addition and
(b) shortly after sample addition. Panel cdescribes the antibody-antigen-signal particle sandwich complex present at the test line for a
positive sample, whereas panel dshows the results for a negative sample. Adapted with permission from Reference 2 under the terms of
the Creative Commons Attribution 4.0 International License, http://creativecommons.org/licenses/by/4.0.
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reagents, and confounders to the matrix (as well as each other), as well as maximizing the visual
signal resulting from the aggregation of analyte–conjugate complexes on the test line. New analyti-
cal methods and advanced materials are being developed every year to improve LFA performance.
Surprisingly, much less effort has gone into advancing our mechanistic understanding of these
assays, despite the growing need to extract higher performance from these tests without added
cost or user interactions.
This review seeks to focus attention on the value that mechanistic models offer in improved
LFA development. A summary of underlying mass transport and reaction theory informs both the
initial development and current approaches to LFA mechanistic theory. The validation of these
models, many of which were developed for alternative assays, is tied directly to their performance in
LFA optimization scenarios. We discuss future directions to improve the quality and demonstrate
the value of mechanistic models to meet the needs and promise that LFA technology holds.
1.1. Current Lateral Flow Assay Development Process
The development of a field-ready LFA that meets sensitivity and specificity goals is a complex
iterative process that is primarily driven by optimizing the various specific and nonspecific mi-
croscale physical and chemical interactions that happen throughout the LFA. Although some of
these interactions can be predicted and modeled, a lack of suitable analytical methods capable of
real-time analysis of LFA behavior, as well as inherent microscale complexity and heterogeneity
of biological samples and reagents, necessitate highly iterative approaches to LFA design.
This iterative development process, comprising four stages, is described by Hsieh and col-
leagues (2) in the flowchart reproduced in Figure 2. The high-level structure of the iterative
process entails the movement from half-stick, to three-quarter stick, to full assay. Typically, it is
at the half-stick stage that the fundamental kinetic performance of an LFA is set. At this stage,
capture and signal antibodies are chosen, as well as conjugation approaches to the nitrocellulose
and signal particle. The method for delivering reagents to the LFA may not be known, or is pushed
back to three-quarter stick development.
A key question and risk that remain at this stage are whether the fundamental materials chosen
during half-stick development will allow the test to meet sensitivity goals, an issue that does not
usually receive full attention until more components are integrated into the test at later stages. The
ability to rapidly mitigate these risks and others at early development stages would meaningfully
reduce the time and cost to develop LFAs and could introduce new design directions for improved
LFA sensitivity.
1.2. Improved Approaches to Lateral Flow Assay Development
Reducing the time to develop LFAs while improving their sensitivity requires augmenting the
current development process with new tools and methods. Hsieh et al. (2) describe a range of
tools and methods being deployed by the FlowDx Group within Global Good to improve the
LFA development process, both internally and in collaboration with partners. One of the tools
recently deployed is an automated LFA optimization system that integrates design of experiments
theory, robotics, miniaturized LFAs, image processing, and statistics into a cohesive system that
can efficiently identify and support the optimization of key factors affecting assay response (3).
In its present state, this system supports the tasks in Stage A shown in Figure 2 through
automated material and reagent screening and optimization protocols. After the best-performing
materials and reagents are identified through screening, an optimization protocol identifies optimal
reagent concentrations through response surface methods. The potential benefits from this type
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Stage 1: half-stick Stage 2: 3/4 stick Stage 3: full assay
Assay complete
NSB minimized?
Field ready?
Antigen
Antibodies
Nanoparticle
Membrane
No
No
No
Yes
Yes
Yes
Wicking pad
Capture antibody on NC
Conjugate
Block on NC
Block on RB
Control line
True matrix
True target
Cover tape
Cassette design
Sample pad
Test reader
Set assay goals
Select best
conditions
Buers
Conjuate Pad
Running buer
Sensitivity/specicity met?
Figure 2
Flowchart describing a typical lateral flow assay design and optimization process. Abbreviations: NC,
nitrocellulose; NSB, nonspecific binding; RB, running buffer. Adapted with permission from Reference 2
under the terms of the Creative Commons Attribution 4.0 International License, http://creativecommons.
org/licenses/by/4.0.
of automation are immense. However, the outcomes are constrained by the process inputs: If the
materials and reagents chosen do not allow the LFA to achieve sensitivity goals, then there is little
for the user to do. In the current development process, this problem is addressed by moving to
different device architectures, revisiting antibody selection, switching to different signal particles,
or manipulating the various buffers used for blocking and running the test.
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1 × 10–7
1 × 10–6
1 × 10–5
1 × 10–4
1 × 10–3
1 × 10–2
1 × 10–1
1 × 101 × 101
Mesoscale
Antibody
Antigen
1 × 1021 × 1011 × 10 1 × 10–1 1 × 10–2 1 × 10–3
Fibrinogen
Full test time
Microscale Macroscale
Timescales (s)
Performance
modication
opportunities
Length
scales (mm)
1 × 103
Distance to
test line
Test line
width
Pore size of
nitrocellulose
Red blood
cell
Malaria parasite
(ring stage)
Standard gold
nanoparticle
Time to
wet strip
Time to
test line
Time at
test line
Time to diuse
across pore
Antigen-antibody
reaction time
Time to advect
across pore
300 μm 3 μm
~5-nm
antigen
~0.7-nm
hydrated
Cl- ion
~7-nm
antibody
~40-nm
gold nanoparticle
Membrane ow rate
Membrane geometry
Sample volume
Reagent concentrations
Reaction duration
Hydrated
salts (Cl)
Sample ltration
Signal particle transport
Membrane pore size, surface area
Antibody anity
Linkers
Signal particles
Surface blocking
Figure 3
Depiction of the various time (top datum) and length (bottom datum) scales within a lateral flow assay, moving left to right from the
macro- to microscale. Scanning electron microscope images towards the center of the graphic illustrate the disparate length scales
between traditional signal particles and nitrocellulose pore sizes.
In practice, pursuing any of these major assay modifications in the middle of development
is expensive. These decisions are often based on previous experience. However, when previous
experience is not available, the LFA development process becomes one of try-until-something-
works. A mechanistic understanding of the key components driving LFA performance is necessary
to add informed guidance to this process.
To fill this gap in the LFA development process, we have developed a mechanistic LFA model
as well as tools and numerical methods to enable the efficient validation of the model. This review
covers the previous modeling efforts that have informed our model, the theory behind these various
models, an applied example, and directions for future development that will enable computational
modeling to better support LFA optimization.
2. REACTION AND MASS TRANSPORT THEORY FOR MODELING
LATERAL FLOW ASSAYS
The processes that make LFAs specific, fast, and sensitive occur over a large range of time and
length scales. Supporting nonobvious LFA optimization through computational modeling requires
that these processes be described mechanistically. The composite diagram in Figure 3 illustrates
the disparate length and timescales present within an LFA and the practical assay components that
can be optimized by modeling approaches that are able to simulate phenomena at those lengths
and timescales.
Until recently, LFAs have been modeled using approaches capable of simulating macroscale
phenomena. Simulation at this scale can support the optimization of strip geometry, assay flow rate,
reagent stoichiometry and delivery format, and signal particle concentration. These macroscale
models fall under the broad category of continuum models, which assume that discrete reactants
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Table 1 Relevant dimensionless numbers of lateral flow assays
Dimensionless number Equation Description
Reynolds (Re) ρLv
μ
inertial forces
viscous forces
Peclet (Pe) Lv
Di
advective flux
diffusive flux
Damk ¨
ohler (Da) L2konCi
DAg
reaction rate
diffusion rate
can be modeled in aggregate as continuous concentrations over dimensions much larger than
the pores of the nitrocellulose matrix. Constitutive equations link continuum models to exter-
nal stimuli, such as Fick’s first law, which relates the diffusive flux of material to concentration
gradients.
Here, continuum approaches to modeling reactions and mass transfer within LFAs are de-
scribed, with the inclusion of failed predictive modes, as this topic has not received detailed treat-
ment within the literature. Finally, future directions for improvement to the continuum modeling
approach for LFAs are identified.
2.1. Characterizing Flow, Mass Transport, and Reaction Regimes
Within Lateral Flow Assays
Dimensionless numbers provide a useful means for characterizing the importance of various trans-
port and reaction processes within biochemical systems and for determining the validity of different
methods for modeling these processes. For LFAs, relevant dimensionless numbers (Tables 1 and
2) include the Reynolds number for describing the nature of flow through the nitrocellulose pores,
the Peclet number for describing the relative rates of advective to diffusive mass transport, and
the Damk ¨
ohler number for describing the relative rates of reaction to diffusion.
Determining values for these dimensionless numbers requires knowledge of the flow rate
through the nitrocellulose pores. Figure 4ashows the flow rate of buffer through Millipore HF120
nitrocellulose. The locations of the four different wetting regimes identified within Figure 4aare
identified in the LFA diagram on the upper portion.
The pore-scale Reynolds number for the LFA in Figure 4aand for LFAs in general is much
less than unity. This suggests that the transport of small-diameter reactants and products from
the free stream to the nitrocellulose pore walls is mainly by diffusion. The diffusion coefficient (D)
for proteins and nanoparticles is approximated by the Stokes-Einstein equation (5):
D=kBT
6πμR.1.
Table 2 Relevant parameter values for lateral flow assays
Parameter Unit Values Description (Reference)
ρg/cm31.0–1.06 Solution density
Lμm5.0–10 Nitrocellulose pore radius (4)
v μm/s100–500 Mean pore velocity
μg/(cm ·s)0.009–0.1 Solution viscosity
Dicm2/s106–108Component diffusivity
kon 1/(M·s)104–107Forward reaction rate
Cing/ml 0.01–1.0 Component concentration
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Hydraulic diameter (nm)
0 50 100 150
Water
Plasma
Whole blood
b
Wetted volume (%)
a
Diusivity (m2/s)
10
–10
10
–11
10
–12
10
–13
10
–14
1.0
0.8
0.6
0.4
0.2
0
Flow rate (μl/s)
Flow duration (s)
0 100 200 300 400 500 600 700 800
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
123 4
123
4
Figure 4
(a) Experimentally measured flow rate through a lateral flow assay (LFA) with a 4-mm by 35-mm Millipore HF120 nitrocellulose
membrane and 22-mm Ahlstrom A320 cellulose wicking pad with a 3-mm overlap. The four different flow regimes segmented by the
red vertical dashed lines correspond to those in the LFA schematic above, namely initial wet-out of the nitrocellulose, wetting of
the nitrocellulose-wick interface, wet-out of the wick, and evaporation from the fully-saturated wick. (b) Diffusion constant as
calculated by Equation 1 plotted as a function of hydraulic diameter (2R) in three diagnostic matrices.
In Equation 1, kBis the Boltzmann constant, Tis solution temperature, μis the solution viscosity,
and Ris the hydraulic radius of the analyte or signal particle. Figure 4bshows the diffusivity of
proteins and nanoparticles in different biological matrices for a range of protein and signal particle
sizes used in LFAs. Two important points are that proteins diffuse much faster than signal particles
and that more viscous matrices like whole blood will significantly decrease the diffusive transport
of all components.
As mentioned earlier, the Peclet number specifies the relative rates of advective to diffusive
mass transport. Figure 4ashows the Peclet number for a 50-kDa protein (5 nm) and two realistic
signal particles (40 nm and 400 nm) over the range of flow rates in Figure 4a. The moderate Peclet
number for proteins and high Peclet number for the nanoparticles suggest that advection timescales
are much shorter than those of diffusion within an LFA. If the timescales for protein and particle
depletion at the test line are shorter than those for diffusion, then the well-mixed assumption
behind simplified continuum models for flow and reaction within an LFA will not be valid.
The Damk ¨
ohler number, which describes the relative rate of reaction to diffusion within
nitrocellulose pores, is determined for LFAs to provide further insight into the validity of the
well-mixed assumption at the pore level. Figure 5bshows the Damk ¨
ohler number plotted against
the association rate constant for a reactant concentration equivalent to 50 pg/ml and 50 ng/ml of
a 50-kDa protein. The pore radius and diffusion constants are the same as in the calculations for
Peclet numbers in Figure 5a.
A rigorous analysis by Battiato & Tartakovsky (6) describes regimes wherein continuum equa-
tions are valid for an advection-diffusion-reaction system. The plot in Figure 5cpresents a graphi-
cal description of their findings, modified to include the ranges of Peclet and Damk ¨
ohler numbers
calculated for the three reactant sizes (5, 40, and 400 nm). This analysis shows that simplified
continuum models will likely not capture the test line binding behavior of larger particles in an
LFA. However, they should be sufficient for proteins (5 nm) and smaller particles (40 nm).
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–2
0
2
4
6
8
10
–10 –8 –6 –4 –2 0 2 4
b
400 nm 40 nm
Predominant reaction
5 nm
c
100 500400300200
5 nm
40 nm
400 nm
a
10
4
10
3
10
2
Peclet number
Pore velocity (μm s
–1
) k
on (M–1s–1)
Damköhler number
10
0
10
–2
10
–4
10
–6
10
–8
10
4
10
5
10
6
10
7
50 ng/ml
50 pg/ml
400 nm
40 nm
5 nm
400 nm
40 nm
5 nm
logε (Da)
ADRE
applicable
ADRE
not applicable
Predominant advection
–logε (Pe)
Figure 5
(a) Pore-scale Peclet numbers calculated by the equation in Table 1 and plotted against pore velocity within the nitrocellulose for
particles with three different hydrodynamic diameters: 5 nm (protein, antibody), 40 nm (traditional gold nanoparticle), and 400 nm
(larger signal particle). (b) Pore-scale Damk ¨
ohler numbers calculated by the equation in Table 1 and plotted against association constant
(kon) for the same particles from panel a. Trends for each of these particles are plotted for both dilute (solid black lines) and concentrated
(dashed blue lines)samples.(c) Plot depicting the ranges for the validity of the advection-dispersion-reaction equation (ADRE), with
overlaid ranges for the particles with hydrodynamic diameters of 5, 40, and 400 nm; the range extents correspond to the intercepts of
the data series in panel bwith the left and right y-axes. Panel adapted with permission from Reference 6. Copyright 2011, Elsevier.
Section 2.3.2 provides further discussion on alternative modeling approaches that can accurately
predict larger particle transport and reaction within porous matrices.
2.2. Macroscale Reaction Theory in Lateral Flow Assays
For many LFAs, the specific ligands and receptors that form the signal complex are antigens
and antibodies, respectively. These noncovalent reversible reactions obey the law of mass action
(LMA), or mass action kinetics, when characterized with the appropriate reaction scheme (see
Section 3.1 for examples). In brief, mass action kinetics describes how the rate of a chemical
reaction relates to the local concentration of reactants (7). For a bimolecular reaction between
antigen and antibody, the reversible reaction is of the form
Ag +Ab kon
koff
AgAb,2.
where kon is the association rate for complex formation, and koff is the dissociation rate constant.
The LMA is only valid for systems with constant kvalues, which implies a single path from
reactants to products on the free energy surface of the system. According to the LMA, the rate of
change of reactant concentration in Equation 3 follows the general form
dCi
dt=kon [Ci][Cii]koff [CiCii],3.
where [Ci] represents unbound reactants, and [CiCii] represents a specific reactant complex. For
reactions at surfaces, Equation 4 takes the form of the Langmuir kinetic equation
dAgAb
dt=konCimax AgAb koffAgAb ,4.
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where AgAb and max are the instantaneous and maximum surface densities of a complex. For
many practical applications in which Equation 4 is used to fit experimental binding data, the
surface concentrations are replaced with volumetric concentrations (8).
Mass action kinetics can explain the reactions within an LFA if the following assumptions are
met: (a) Kinetic rate constants are constant with concentration, which is true for dilute systems
and typical LFA systems of interest for modeling; (b) binding does not alter the ligand or receptor,
which is true when multivalency is accounted for in the reaction network (8, 9); and (c) the volume
is well mixed, which is true under pore-scale criteria (see Section 2.1). For liquid-solid interface
reactions with large liquid-phase nanoparticles, LMAs may invalidate the well-mixed assumption,
as shown by the 400-nm particles in Figure 5c. This issue can be addressed by switching to a
two-compartment approach, whereby an additional rate equation is paired with Equation 3 to
represent the nanoparticles movement from the bulk to the reaction compartment (10).
The use of mass action kinetics to describe ligand and receptor binding in LFAs is a major
simplification of the chemical interactions occurring within the assay, which includes hydrogen
bonds, ionic forces, and conformational changes (11). Generally, when the assumptions behind
mass action kinetics are met, this simple and efficient approach has been shown to accurately
describe LFA behavior (12, 13). Alternative theory must be applied in cases wherein mass action
kinetics cannot explain reactant binding behavior (14); Section 2.3.2 addresses alternatives to mass
action kinetics for signal particle binding.
2.3. Mass Transport Theory in Lateral Flow Assays
The transport of reactants through the nitrocellulose membrane to test line receptors is essential
to LFA function. This section provides a continuum description of mass transfer within LFAs.
Alternatives to the continuum description are presented for the case in which the continuum
approximation fails to describe binding of large signal particles to receptors at the test line.
2.3.1. Advection, diffusion, and dispersion of reactants within lateral flow assays. The
movement of reactants in an LFA from the location of sample input to the test line occurs through
advection, diffusion, and kinematic dispersion. Advection describes the movement of reactants by
the bulk motion of the liquid and is of importance mainly within the nitrocellulose membrane
because flow rates are much lower in the sample and conjugate pads after initial wetting.
The diffusion of reactants by Brownian motion is driven by concentration gradients, with
reactants moving from regions of higher to lower concentration. The porous nature of the ni-
trocellulose membranes used in LFAs leads to a reduction in the diffusion coefficient over that
measured in free solution (15–17). The effective diffusion coefficient for reactant ican be defined
as
Deff,i=
τDi,5.
where is the porosity of the material, τis the material tortuosity, and Diis the free solution
diffusion coefficient for reactant i. The material tortuosity can be estimated by a number of
approximate models, such as that of Millington and Quirk (18), where τ=1/3.
Kinematic dispersion is the spreading of reactants along the direction of flow by the het-
erogeneous porosity of the nitrocellulose matrix, which leads to variability in the microscopic
pore velocities. Kinematic dispersion is combined with the diffusion coefficient to form the dis-
persion coefficient. Advection and dispersion contributions to reactant transport are combined to
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describe the overall transport of reactants through the LFA in the form of the advection-dispersion
equation:
dCi
dt=Ddisp2CiνCi,6.
where is the porosity of the material, Ciis the concentration of reactant i,vis the superficial
velocity vector, and Ddisp is the dispersion coefficient, defined as Ddisp =Di+αLv,whereαLis the
longitudinal dispersivity. Determining a value for αLis nontrivial, requiring an experimental setup
similar to that described by Ahmad et al. (19). Numerous correlations have been proposed for pre-
dicting αL(20), but the accuracy of these correlations has not been assessed for reactant transport in
LFAs.
2.3.2. Nanoparticle transport in nitrocellulose. Nanoparticles exhibit unique transport prop-
erties in porous media, sharing some of the transport behaviors of both smaller protein reactants
and larger colloids. Most of the theory developed to understand nanoparticle transport in porous
media has come from the field of hydrogeology, where the goal has been to upscale pore-level
reaction and deposition behavior to the Darcy scale (21, 22).
Predictive models for colloid transport are primarily based upon the Equation 6 for non-reactive
transport, and Equation 9 for reactive transport. However, instead of accounting for nanoparticle
binding on pore surfaces through a constant association term as in mass action kinetics, colloid
filtration theory (CFT) accounts for binding through a combination of mechanistic and empirical
terms that are dependent on the particle, pore, and flow rate parameters.
Many different CFT models have been developed, each with different treatments of the cor-
relation equations that predict collector contact efficiency, η, defined as the fraction of colloids
entering a mechanistic model geometry that contact the pore wall (23). The collector contact
efficiency is defined as η=αη0,whereαis the attachment efficiency, describing the probability
of pore-wall attachment after a collision, and η0describes the transport of particles from the bulk
fluid to the pore wall.
The pore-level transport term is usually composed of contributions from three different in-
terrelated mechanisms, namely pore-wall interception via fluid drag (ηI), diffusion-enhanced in-
terception (ηD), and sedimentation-enhanced interception (ηG), such that η0=ηI+ηD+ηG.
Pore-wall collisions by sedimentation are negligible for nanoparticle systems of interest here, and
therefore, η0is considered to be only a function of ηIand ηD.
The collector contact efficiency is implemented in continuum models, specifically the
advection-dispersion-reaction equation (ADRE) (24), by replacing the association rate constant
from Equation 3 with a parameter that is a function of the pore velocity, average pore collector
diameter, porosity, and the collector contact efficiency. The functional form of the association rate
constant is different for the various contact collector efficiency correlations (23), and in almost all
cases, αmust be determined by fitting the model to experimental data.
The practicality of applying CFT for modeling larger nanoparticle transport and binding in
LFAs requires having a generalized form for η0that can be determined through the combination
of measurable experimental parameters and variables easily determined from a continuum model.
Boccardo et al. (25) used detailed models to develop a more generalized form for η0that fit data
for different particles sizes, flow rates, and pore geometries. The model by these authors provides
a promising direction for the accurate and efficient integration of large nanoparticle transport into
continuum models for LFAs. However, more work needs to be done to verify the accuracy of this
approach for LFAs.
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2.4. Coupled Mass Transport and Reaction Theory in Lateral Flow Assays
Functional LFAs result from numerous mass transfer–driven reactions reaching a favorable state of
completion before their capture at a test line. This section provides an overview of the theory that
governs the analyte-mediated formation and subsequent capture of quantifiable signal complexes.
2.4.1. Antigen binding to antibody-coated nanoparticles in solution. In most commercial
LFAs, the patient sample is deposited directly onto dried-down signal particles just prior to the
upstream addition of running buffer. Adding sample and buffer to the LFA in this way leads to
a majority of the test line signal coming from antigen-signal particle complexes, particularly for
samples with low antigen concentrations. The liquid-phase reaction of antigen with an antibody-
coated nanoparticle maps to the generalized scenario of reversible ligand binding to cell surface
receptors. The theory of ligand binding to cell surface receptors is well developed; it was initially
explained by Berg & Purcell (26) and since extended (27) and validated (28) by others. The effective
on and off rates from this theory are:
kon,particle =4πaDNkon
Nkon +4πaD ,7.
koff,particle =koff 14πaDNkon
Nkon +4πaD ,8.
where ais the cell radius, Nis the number of receptors on the cell surface, Dis the diffusion
coefficient for the ligand, and kon and koff are the intrinsic on and off rates for the ligand-receptor
pair [such as those measured by surface plasmon resonance (SPR) or biolayer interferometry
(BLI)]. These kinetic constants can be combined with mass action kinetic models to describe the
concentration of ligands bound to a spherical particle (29–31).
An important caveat to the terms in Equations 7 and 8 is that their derivation does not take
into consideration local concentration effects or specifics of the ligand-receptor binding event.
Higher-fidelity information about the specifics of the ligand-receptor reaction at the nanoparticle
surface requires computationally expensive molecular dynamics simulations (32–35). Nonethe-
less, simplified mass action kinetic models have been shown to sufficiently explain experimentally
measured bulk-scale binding behaviors on nanoparticles (36).
2.4.2. The transport and binding of antigen, nanoparticles, and antigen-nanoparticle
complexes to test line receptors. The formation of signal particle complexes at the test line can
occur by a number of reaction routes. The two main routes are by binding of antigen-nanoparticle
complexes to available test line receptors (typically antibodies), or by a sequential binding reaction,
where antigen binds to the test line receptor, and a nanoparticle binds to the antigen-receptor
complex.
The bulk transport of all of these reactants and complexes through the nitrocellulose pores to
the test line can be described by Equation 6. From the analysis in Section 2.1, sample antigen is
assumed to be well mixed at the pore level, and therefore no additional terms must be added to
Equation 6 to account for antigen transport from the bulk to the test line receptor. The transport
and reaction of antigen leading up to and at the test line are then described by the ADRE
dCi
dt=Ddisp2CiνCi+Ri,9.
where Riis the local rate of change of antigen due to the reaction described by Equation 3. The
actual amount of unique reactions irepresented by Riin Equation 9 can be large for a standard
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sandwich LFA. However, in the authors’ experience, a reduced subset of reactions is usually
sufficient to explain the bulk of the reactions required to generate the test line signal.
Test line receptors are assumed to be volumetrically distributed throughout the pore volume.
In reality, receptors are attached to the pore-wall surface. Additional terms may need to be added
to Equation 9 to account for mass transfer effects for nanoparticles or antigen-nanoparticle com-
plexes. Improved predictive accuracy for the transport and binding of larger nanoparticles to test
line receptors is enabled by coarse-grained approaches that track particles as discrete entities in
time that collide with and bind to geometrically realistic surfaces (37–41).
3. DEVELOPMENTS IN THE MODELING OF LATERAL FLOW ASSAYS
Advanced applications of computational modeling are now helping us to better understand and
improve the performance of LFAs. Much of the underlying foundational theory and approach for
modeling LFAs comes from earlier simulations of the performance of enzyme-linked immunosor-
bent assays (ELISAs), microfluidic immunoassays, and flow in porous media. The following sec-
tions provide a historical summary of this foundational theory and its application toward modeling
LFAs.
3.1. Immunoassay Models
The mathematical theory of radioimmunoassays was published by Berson and Yalow in the late
1950s (42, 43). Later, Rodbard and colleagues (44–46) would integrate this theory into compu-
tational models to understand the dynamics of radioimmunoassays under a range of boundary
conditions. Significant advances in immunoassay theory over the next two decades are summa-
rized by Stenberg & Nygren (47), who also introduce a more detailed description of the interplay
between liquid-phase diffusion and reaction at the solid-liquid interface within nonequilibrium
ELISAs. Paek & Schramm (48) validated this extended theory by showing close alignment between
an experimental progesterone ELISA and its computational model. This model was then used to
identify optimal assay conditions under nonequilibrium conditions (49). Sadana and colleagues
(50, 51) extended the analysis from Stenberg and Nygren to higher-order reaction systems and
solid-phase immunoassays with nonspecific binding (52, 53). Bicskei et al. (54) demonstrated the
predictive capabilities of mass action–based immunoassay models by accurately estimating the
concentrations of unknown samples with a model that had been calibrated against kinetic data
from a single experiment. Ylander and colleagues (55, 56) introduced a more intuitive node-based
method for formulating kinetic immunoassay models and then used it to explore different aspects
of immunoassays, including nonspecific binding.
Avella-Oliver et al. (57) integrated existing ligand-receptor mass transfer theory with mass ac-
tion kinetics into a flexible user-friendly tool for characterizing and optimizing various biorecog-
nition assays in silico. The novel contribution from this work was their articulation of how their
model could be used as an in silico lab bench to identify information about assay performance
and reaction mechanisms that was otherwise unachievable at a physical lab bench. Lewin et al.
(58) conducted a detailed study on bidirectional interference in immunoassays using a mass ac-
tion kinetics model. The study showed the circumstances under which bidirectional interference
can arise and the potential utility of modeling tools to elucidate the mechanisms of nonspe-
cific binding. Recently, Sotnikov et al. (59) published a review on mathematical modeling of
bioassays that covered a breadth of applied theory relevant to model-supported immunoassay
design.
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3.2. Fluid Flow Models for Paper Microfluidics
Fluid flow is an essential component of LFAs and other paper-based microfluidics, enabling the
transport of assay components from the sample and conjugate pads to the test line receptors.
Flow optimization is therefore essential for achieving the true limit of detection for an LFA.
Computational models have proven to be both accurate and tractable tools for supporting these
optimization efforts.
Two general modeling approaches based on the mean-property assumption (60) have been
shown to accurately predict flows in paper-based microfluidics. These include the capillary model
of Lucas and Washburn, and porous-continuum models based on Darcy’s law, and the continuity
equation. Capillary models for flow in porous media describe wetted length as a function of time
twith the Lucas-Washburn equation (61, 62):
L(t)=γcos θ
2μrct, 10.
where μis the liquid viscosity, γis the liquid surface tension, θis the contact angle, and rcis
the equivalent capillary radius. Various studies have demonstrated the accuracy of the Lucas-
Washburn equation for predicting wetting behaviors in paper materials with constant cross-
sectional area (63, 64). Toley et al. (65) used the Lucas-Washburn equation along with an electrical
circuit model to predict delayed reagent delivery in a paper-based device with flow shunts. Ad-
ditional applications of capillary-based modeling of flow in paper are summarized in depth by
Perez-Cruz et al. (66).
Models based on Darcy’s law and the continuity equation can much more accurately simulate
multimaterial wetting scenarios in more complicated paper architectures. Darcy’s law for flow of
a single liquid in an isotropic porous medium and the macroscopic continuity equation are shown
in Equations 11 and 12, respectively:
˜
v=−K
μP, 11.
∇·˜
v=0, 12.
where ˜
vis the volume-averaged liquid velocity, Kis the permeability of the porous medium, μis
the liquid viscosity, and Pis the pore-averaged modified pressure, defined as P=p+ρgh,where
pis the hydrodynamic pressure, gis the acceleration due to gravity, and his the coordinate height
of a point porous medium. Appropriately calibrated Darcy’s law models are generally better at
predicting wetting behaviors than those based on Lucas-Washburn theory (67–71). Mendez et al.
(72) and Elizalde et al. (73) demonstrated how two-dimensional (2D) Darcy’s law models can be
used to identify nonintuitive 2D membrane shapes that provide desired temporal flow profiles.
Darcy’s law assumes a uniform pore size and complete wetting behind the liquid front. How-
ever, recent studies of wetting and flow in paper systems have demonstrated that the pores behind
the wetting front are not saturated, in part due to the pore structure heterogeneity (74). The
Richards equation, well known in the hydrogeology field, has recently been applied to model
capillary flows in paper-based microfluidic materials to address shortcomings of Darcy’s law in
simulating partially saturated flow (66, 75). The Richards equation with gravitational effects ne-
glected is shown in Equation 13:
dθ
dt=∇[K(θ)ψ(θ)], 13.
where θrepresents the volumetric content of liquid, K(θ) is the equivalent fluid conductivity, and
ψ(θ) is the capillary pressure head. The equivalent fluid conductivity is approximated by various
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models that must be fit either to experimental water retention curves or to experimental flow data
using an optimization routine. Recent work by Buser (75) and Perez-Cruz et al. (66) describes
the use of Richard’s equation to accurately predict flow in 2D geometries of practical interest for
POC device design. Developments by Perez-Cruz et al. show how the typically time-consuming
process of identifying unknown model parameters can be simplified through automation. The
modeling approaches described in these studies demonstrate a promising path forward for flow
optimization within LFAs.
3.3. Lateral Flow Assay Models
The use of computational modeling to characterize and optimize LFA performance is relatively
new. The recent increase in LFA modeling studies reflects the growing demands of the LFA market
for tests that provide more quantitative detail and greater sensitivity. The following review covers
developments in the two main approaches to modeling LFAs, ADRE models, and nonlinear state-
space models.
3.3.1. Advection-dispersion-reaction equation models. Most of the approaches to model-
ing LFAs to date have been based on the ADRE. Early implementations of this approach by
Krishnamoorthy et al. (76), Qian and colleagues (77, 78), and later Ragavendar & Anmol (79)
were aimed at providing guidance on improved LFA sensitivity, mainly through manipulation
of test line location and flow rates. Mass action kinetics were assumed for the reactions within
all of these models, with models by Qian and colleagues and Ragavendar and Anmol assuming
pseudo-first-order reversible reaction kinetics. Although these studies provided useful qualita-
tive linkages between design parameters and test line intensity, none of them were quantitatively
validated.
Liang et al. (12) were the first to quantitatively validate an LFA model based on the ADRE
in Equation 9. They did this by improving the fidelity of model inputs, identifying unknown
parameters by fitting the model to high-fidelity experimental data, and generating a calibration
curve to map model units to optically measureable units from an experimental LFA. They used
this model to mechanistically explain the lower limit of detection achieved by an experimental
LFA run with sequential reagent delivery. One of the underlying assumptions behind this study
was that kinetic values measured by SPR could be used for all but one of the kinetic parameters.
Mosley et al. (80) demonstrated that kinetic parameters measured through SPR do not repre-
sent the kinetics of the parameters in an LFA. Specifically, they found that SPR measurements
significantly overpredicted the forward reaction rate constants that were subsequently measured
within an LFA. The rate constants within the LFA were measured using a novel approach whereby
reagents were tagged with radioactive iodine-125 and measured at the LFA test line at different
time points. Kinetic parameters were determined by fitting the temporal test line data to a mass
action kinetics model. Besides quantitatively verifying the large offset between kinetics measured
through SPR and those within an LFA, their modeling approach was also the first time that sig-
nal particle multivalancy was included in an LFA model. Liu et al. (81) later incorporated the
multivalent signal particle modeling with the one-dimensional (1D) ADRE to optimize the con-
centration of binding site density on signal particles for an HIV nucleic acid LFA. The model was
qualitatively validated against experimental data.
Several recent publications describe LFA models with increasing spatial fidelity and improved
validation methods. Schaumburg et al. (82) developed three-dimensional (3D) LFA models based
upon the ADRE with mass action kinetics. They performed a qualitative validation of the 3D
model against an experimental LFA, demonstrating that the model could recreate the test line
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development characteristics seen experimentally. The pre-nitrocellulose zones of LFAs are diffi-
cult to explore experimentally, and their multimembrane model provides a promising approach
to understanding critical mixing and reaction phenomena in this area. Zhan et al. (13) developed
a 2D LFA model based on the ADRE with mass action kinetics to study how signal particle size
impacted signal particle binding at the test line for a C-reactive protein LFA. They quantitatively
validated this model for various sized signal particles by aligning model and experimental data
with kinetic parameter fitting. The fitting used a calibration curve to link the signal complex con-
centration at the test line to the signal value measured with their thermal contrast reader LFA
reader. Additional considerations in their model validation process provide useful guidance for
more quantitative LFA modeling.
Finally, LFA models based on a simplified form of the ADRE can provide qualitative insights
to guide LFA optimization. Berli & Kler (83) developed a simplified analytical LFA model for
predicting antigen binding at the test line and used the model to generate two dimensionless
numbers for design optimization: the relative flow rate and the relative analyte concentration.
Sotnikov et al. (84) developed an analytical model of a serodiagnostic LFA that was used to
identify optimal sample volume, dilution, and test line antigen for optimal test performance. The
model by Sotnikov et al. was qualitatively validated against experimental data and later extended to
investigate two reagent delivery designs for the same serodiagnostic (85). The models were used
to mechanistically explain the differing experimental performance observed for the two reagent
delivery designs, and then used to probe the LFAs sensitivity to various model parameters.
3.3.2. Nonlinear state-space models. Zeng and colleagues (86) developed an alternative ap-
proach to modeling LFAs using nonlinear state-space models. Their approach assumes that the
system of reactions within an LFA can be described by a nonlinear state-space system that is char-
acterized by state and observation equations. Their system-state equations describe the dynamics
of reactant and complex concentrations subjected to stochastic disturbances, and the measureable
signal from the assay is described by an observation equation containing measurement noise (86).
The state-space LFA modeling approach shares important similarities to the ADRE LFA models,
namely that reaction schemes must be identified up front and that unknown model parameters
must be identified through model validation with experimental data. The process for defining
state-space equations and unknown parameters is described in detail elsewhere (86). Once de-
fined, the goal is to determine unknown parameter values that provide the best fit between model
and experimental test line signal intensity for all time points, while considering uncertainties in
both the model and measurements.
Initially, Zeng et al. (86) applied an extended Kalman filter (EKF) algorithm to jointly estimate
the system states and parameters for the LFA, using the optically measured peak value of the test
line over a range of time points as the validation data set. Their subsequent publications focused
on replacing the EKF approach with approaches that were better suited to deal with the highly
nonlinear nature of LFAs. These included a particle filtering algorithm and kernel smoothing
method (87), a hybrid extended EKF and switching particle swarm optimization algorithm (88),
an expectation maximization algorithm (89), and a particle swarm optimization method based
on nonhomogeneous Markov chain and differential evolution (90). Importantly, the time delay
between the application of assay reagents and the appearance of the test line was not captured by
the model structure in these previous analyses. To address this shortcoming, Zeng et al. (91, 92)
have since updated their nonlinear state-space modeling approach to include time delays in the
state-space and signal measurement equations using improved algorithms.
The nonlinear state-space approach developed by Zeng and colleagues (91, 92) is a novel
and potentially effective approach for predicting test line development for LFAs with fully
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characterized delays. It does, however, require further development before it can be applied as a
practical design tool for those at the bench developing and optimizing LFAs. Namely, the method
must be capable of characterizing aspects of the LFA that can realistically be modified by the
designer. For example, the link between the lag time parameter and the nitrocellulose membrane
is still too abstract to be useful for design purposes (91, 92). The closing of these usability gaps
could enable the nonlinear state-space modeling approach to be an effective characterization and
design tool for LFA developers.
4. MODELING A MALARIA ANTIGEN LATERAL FLOW ASSAY
Malaria, caused by Plasmodium parasites, continues to be a leading cause of death in the developing
world, with an estimated 429,000 deaths in 2015 (93). Since their introduction in the 1990s, LFAs
have been a critical tool for diagnosing malaria in low-resource settings (94). Plasmodium lactate
dehydrogenase (pLDH) is the main biomarker for active malaria infection by malaria species apart
from the dominant Plasmodium falciparum. The current commercial LFAs designed to detect the
pLDH biomarker are lacking in sensitivity, and ongoing efforts by multiple groups are focused on
improving this sensitivity (95). We present a continuum model validation against experimental data
to demonstrate an efficient process for accurately predicting important directions for improving
assay sensitivity.
4.1. Lateral Flow Assay Model Definition
The basis of this pLDH LFA model is to determine if assay performance can be accurately pre-
dicted by a reduced set of reactions derived from a typical starting scenario. Primary simplification
is based on the assumption that flow and reaction behaviors across the test strip width and depth
are reasonably uniform and can be represented in a 1D domain, as shown in Figure 6a. Chemical
interactions are reduced to six kinetically defined complex formations.
abc
1,000
2,000
3,000
4,000
0
LFA optical reader signal units
Test line
Reactions
in solution
40-nm gold particles
(mol/m3) in nitrocellulose
10–6
10–7
10–8
Test line
reactions
Simplied
computational
domain (1D)
ka,1
kd,1
ka,6
kd,6
ka,2 kd,2
kd,4
ka,4
a,4
4
,
k
k
k
kd,5
ka,5
ka,3
kd,3
10–5
10–10
10–15 Units = mol/m3
Figure 6
(a) A description of the simplified computational lateral flow assay (LFA) domain used for the modeling in this section, along with the
simplified reaction set tracked by the model in solution and at the test line. (b) Example of model results, showing the specific
concentrations of various reactants and complexes present during the test, based on the reaction scheme in panel a.(c) Optical
calibration curve for translating molar concentration units from the model into optical signal units output by the Axxin LFA reader.
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The ADRE (see Equation 9) describes the movement and reaction of species throughout the
1D domain, with reactions in Figure 6adescribed by mass action kinetic formulations. A time-
dependent experimentally measured flow rate is prescribed throughout the domain, similar to the
flow rate in Figure 4a. Sample antigen (pLDH) and nanoparticle volumes and concentrations
are prescribed in the domain adjacent to the test inlet (effectively, the sample pad). Similar to
the behavior of a physical LFA, the model simulates reactions within the sample and conjugate
pads while the solution is metered onto the LFA. An ordinary differential equation tracks species
concentrations in the sample pad, with the species value in this domain acting as the species inlet
value to the nitrocellulose domain. The initial concentration of receptor antibody at the test line
is approximated by a smoothed rectangular step function (96).
As the simulation proceeds in time, the model tracks six different species; a snapshot of the
concentration of these different species 60 s into the test is shown in Figure 6b. In general, unbound
test line antibody is in significant excess, followed by signal particles. Molar concentrations of
signal particle complexes at the test line are converted to optical reader units (Axxin LFA reader,
Fairfield, Australia) for model validation using the calibration curve in Figure 6c.
4.2. Model Validation
The validation process for the LFA model presented here has two objectives: First, verify the
assumed reaction scheme, and second, identify unknown and unmeasurable model parameters
that provide the best fit between model and reality. These objectives are coupled, making the
process iterative if the initial reaction hypothesis is incorrect. Figure 7 describes the mechanics
of the validation process and how it ties into the optimization goals for the model.
Model parameters
No model t
Flow rate data
Optical reader
Flow rate
measurement
Model validation process
LFA model
Reaction network
hypothesis
Material, reagent
and design updates
Parameters, driving
test, sensitivity
Validated
LFA model
Sensitivity,
analysis,
parameters
LFA design
Experimental
LFA data
Experimental
data tting
Fitted
model
LFA optimization process
0
2,000
4,000
6,000
8,000
Figure 7
Flowchart describing the quantitative lateral flow assay (LFA) model validation process (top) and how the model integrates with the
LFA optimization process (bottom). The validation process requires the generation of various input data for the validated model to
provide quantitative predictions. This data includes flow rate measurements within the membranes of interest, optical test line
measurements with a high-sensitivity optical LFA reader, and the generation of an optical calibration curve that maps signal particle
concentration at the test line into optical LFA reader units. Once a model is validated over the appropriate parameter space, it can be
run through a series of design studies to identify test design parameters for optimal test line signal.
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The validation process begins by running a series of pLDH LFAs with different antigen con-
centrations and converting the test lines into a 1D-intensity profile using an optical reader (Axxin
AX-2X). The pLDH LFA computational model was implemented in COMSOL Multiphysics
(COMSOL, Inc., Burlington, Massachusetts) as a time-dependent, 1D simulation. An optimiza-
tion routine using the BOBYQA method (97) integrates with the time-dependent simulation to
determine kinetic binding coefficients, test line antibody activity, and conjugate concentration
that allow for best fit between model and experimental data. Nuances to the validation process
will be presented in a future publication.
The model fit to experiment was exceptional over the pLDH concentrations tested, as shown
in Figure 8a. To demonstrate the model’s predictive utility, a separate experimental LFA series
Signal
complex
Flow
Step 1
Signal
complex
Signal
particles
Flow
Step 1 Step 2
Distance along test lineDistance along test line
Reactions
Reactions
a
b
Experiment
Model
pLDH
antibody
Antigen–
signal particle
complex
pLDH
(antigen)
6.25
ng/ml
3.125
ng/ml
25 ng/ml
12.5
ng/ml
Scaled test line intensity
(measured on optical reader)
Scaled test line intensity
(measured on optical reader)
Experiment
Model
3.125
ng/ml
6.25
ng/ml
25 ng/ml
12.5
ng/ml
Antibody–
antigen
complex
pLDH
(antigen)
pLDH
antibody
Figure 8
(a) Model reactions and experiment description (left) for the validation of the six-reaction pLDH lateral flow
assay model. The test line profile from experimental (dashed red line) and model (solid black line)dataareshown
for in the inset plot. (b) Model reactions and experiment description for the validation of the parameters
from panel ain a reduced reaction system. Abbreviation: pLDH, Plasmodium lactate dehydrogenase.
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1.0 1.2 1.4 1.6
Sample volume (μl)
ka,4
Capture antibody activity
Flow rate ½×
ka,2
NP concentration (p/ml)
ka,3
Flow delay (s) 60s
ka,1
Experiment
Model
Factor improvement over baseline
(as measured by optical reader)
Figure 9
Factor of improvement over the baseline pLDH model for various perturbations to the model parameters as
predicted by the validated model (blue horizontal bars), alongside experimentally measured factors (boxes) of
improvement for a 2×increase in sample volume and nanoparticle (NP) concentration, and a 60-s increase
in flow delay down the strip. A value less than one indicates a decrease in test line signal between the baseline
condition and the perturbed condition.
was run with the same reagents delivered in a more operationally complex sequential format. This
removed the possibility of four of the six previously modeled reactions. The pLDH LFA model
was modified to replicate this sequential delivery, using the parameters derived from the initial
experiment. The overlay results from this system are shown in Figure 8b, demonstrating that the
validated six-reaction model can accurately predict reagent performance in different LFA formats.
4.3. Identifying Critical Assay Parameters
The validated pLDH model was run through a sensitivity analysis to identify the parameters
that most affected the test line signal at low pLDH concentrations. Physically realistic values
were chosen for the perturbation of each assay parameter based on constraints that the test
(a) be rapid (flow rate, sample volume, flow delay), (b) have minimal nonspecific binding (NSB)
(nanoparticle concentration, capture antibody activity), and (c) have antibody kinetics that are real-
istically achievable (kinetic constants). The perturbation values from this last requirement were es-
timated based on realistic improvements in antibody binding kinetics that can be achieved through
a round of antibody selection (98). The results of this sensitivity analysis are shown in Figure 9.
Three additional experiments were run to verify model predictions for increasing nanoparticle
concentration, sample volume, and incubation time. Figure 9 shows a close alignment between
model prediction and experimental measurement for these parameters.
This example is not meant to be exhaustive, yet this simple analysis already points toward
important development narratives for this assay. For example, creating more antigen-bound signal
particles in solution is not the direction to take for improved sensitivity for this assay. Additionally,
working to improve the limiting reaction in the assay—the binding of particles to the test line
(ka,3)—will only begin to markedly improve sensitivity after dramatic improvements in binding.
Practical improvements in all other parameters will also only have a moderate effect on sensitivity.
Therefore, radical improvements to ka,3 are needed, for example, through the biotin-streptavidin
reaction. Approaches should be considered to improve ka,4, which represents the binding of signal
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particles to antigen that is already laid down at the test line, perhaps via different particle sizes
(99). The next obvious step with this analysis would be to look into multiparameter perturbations
to determine if moderate improvements in two or more parameters could lead to improvements
larger than the sum of their parts.
4.4. Additional Directions for the pLDH Lateral Flow Assay Model
The preceding case study demonstrates the accuracy with which a reduced-complexity model can
capture the macroscale behaviors of a physical LFA and identify critical test parameters. Note that
this study was constrained to only a subset of all LFA parameters that could potentially be explored.
For example, alternative nanoparticles could be explored with their respective calibration curves
and heuristics for how particle kinetics scale with particle size. Additionally, alternative reaction
schemes could substitute known chemistry. Essential to this modeling approach is that it improves
design decisions quickly and more affordably than doing the tests by hand. Computational sampling
of a larger solution space also reduces the probability that optimization is closing on local rather
than global minima. However, it is clear that manual validation of a model can be unattractively
lengthy. We address this in the next section by demonstrating tools that we have made to speed
up this process.
5. CONCLUSIONS AND OUTLOOK
5.1. Practical Integration of Modeling into the Lateral Flow Assay
Development Process
Computational modeling is used extensively to support the design of biochemical sensors and
diagnostics (100–104). Its use is justified because it either saves time and money in relation to
benchtop experimentation or because it can elucidate phenomena and trends relevant for device
design beyond what is possible with experimentation. Computational modeling of LFAs is no
different, provided the model is sufficiently accurate for the design task, and the model validation,
sensitivity, and design analyses are more efficient than experiments for the same outcome. We have
developed a software implementation of the LFA model described in Section 4, with capabilities
that address the abovementioned requirements. A screen capture of the prototype application is
shown in Figure 10a.
The software application enables users to explore a range of reaction scheme hypotheses by
choosing from 15 different reactions, as shown in Figure 10b. Once a reaction scheme is chosen,
the application significantly speeds up the validation process by automating the alignment of
experimental data with the model representation. It does this both prior to starting a validation
simulation and during the simulation at prescribed iteration counts. If the model cannot find an
adequate fit to the experimental data, then users can iteratively test alternative reaction schemes.
With a validated model, the application can use the best-fit parameters to run sensitivity or what-if
scenarios for probing parameter sensitivity or hypothetical design scenarios, respectively.
Although sensitivity analyses and what-if modeling can reduce front-end development time for
LFAs, back-end development time is frequently monopolized by characterizing and solving issues
with NSB. The LFA application described here cannot provide guidance on buffer selection
for reducing NSB by design, but it can provide a means for characterizing the mode of NSB,
which can focus development efforts toward the pertinent source. Our application supports NSB
characterization by providing the user with seven different NSB-related reactions that lead to lost
antigen or nonspecifically bound signal particles. Hypothesis testing is still user driven; however,
23.20 Gasperino et al.
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ba
Flow
Figure 10
(a) Screenshot of the lateral flow assay (LFA) modeling tool developed by the Global Good FlowDx group for supporting LFA model
validation and predictive simulation of LFA performance. (b) Dialogue box showing user-selectable reaction schemes for model
validation or predictive simulation.
the approach could be automated to incrementally add reaction complexity to an initially simple
reaction framework (105, 106).
5.2. Important Directions for the Development of Immunoassay Theory
as a Tool for Assay Design and Improvement
The main LFA modeling approach covered in this review describes macroscopic assay behavior.
As discussed in Section 2, simplifications that make this type of macroscale modeling tractable
and efficient come at the price of physical fidelity at smaller length scales. This reduces the design
insight that the model can provide. Two broad development directions can dramatically extend
the capacity of this modeling approach to support nonintuitive aspects of LFA design. The first
of these improves specific aspects of model fidelity through coupling to microscale phenomena,
whereas the second extends the macroscopic modeling approach to more complicated reaction
schemes. We discuss salient aspects for each approach below.
The current macroscale LFA model should benefit from a more detailed treatment of nanopar-
ticle transport and binding to the test line. As covered in Section 2.3.2, numerous ADRE models
simulate nanoparticle binding to ligands within porous domains. Once validated, many of these
models do not extrapolate to even moderately different systems (107). A primary reason for this
is the lower diffusivities of larger nanoparticles, which deviate from the “well-mixed” assumption
at the pore scale (108). Lagrangian particle modeling can overcome these limitations (41, 109).
In LFA design work, the effect of spatiotemporal solution properties on antigen–antibody bind-
ing is another important and often overlooked microscale consideration. The solution components
that affect antigen–antibody binding subject to spatiotemporal variations include pH, salinity,
detergent, surfactant, and protein blocker. Empirical input–output testing is often used to deter-
mine the concentrations, and in some cases, the locations at which components should be applied
to the test. However, these determinations are potentially misleading, as they likely represent the
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best performance of a nonideal system. These profiles can be contextualized using advanced flow
modeling described in Section 3.2 and ADRE modeling. This can provide insight into how far from
ideal the LFA design is and the robustness of solution composition assumptions. Optimization rou-
tines could then be tested to identify reagent application approaches that would lead to more ideal
spatiotemporal reagent concentrations and improve sensitivity and reduce nonspecific binding.
Finally, recent modifications to the traditional LFA reaction format at the macroscale
level demonstrate novel pathways to dramatic improvements to LFA sensitivity through signal
enhancement (110), solution-phase reaction schemes (111), and antigen concentration approaches
(112, 113). These various directions for sensitivity improvement of the LFA platform provide in-
spiration that the field of LFA development can continue to move into more use cases in areas
that need low-cost, easy-to-use diagnostics. With continued development, the modeling approach
described in Section 4 can support optimization with these new methods and potentially identify
the next generation of novel test formats.
With sufficient effort, we anticipate that computational models are poised to provide the bench
experimentalist with a powerful tool to more efficiently explore solution space within an ever-
growing catalog of materials. By contextualizing results within a theoretical performance matrix,
future efforts can be efficiently directed toward the optimizations that will deliver LFAs that
achieve their full potential.
DISCLOSURE STATEMENT
The authors are not aware of any affiliations, memberships, funding, or financial holdings that
might be perceived as affecting the objectivity of this review.
ACKNOWLEDGMENTS
Funding was provided by The Global Good Fund I, LCC (www.globalgood.com).
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