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RAPID ESTIMATION OF ANTIBIOTIC EFFICACY OF LOW
BACTERIAL INOCULUMS USING MULTI-FREQUENCY
IMPEDANCE MEASUREMENTS
_______________________________________
A Thesis
presented to
the Faculty of the Graduate School
at the University of Missouri-Columbia
_______________________________________________________
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
_____________________________________________________
by
NICHOLAS COLONA
Dr. Shramik Sengupta, Thesis Supervisor
JULY 2015
The undersigned, appointed by the dean of the Graduate School,
have examined the Thesis entitled
RAPID ESTIMATION OF ANTIBIOTIC EFFICACY OF LOW
BACTERIAL INOCULUMS USING MULTI-FREQUENCY
IMPEDANCE MEASUREMENTS
Presented by Nicholas Colona
A candidate for the degree of Masters of Science and hereby certify
that, in their opinion, it is worthy of acceptance.
___________________________________________________
Dr. Shramik Sengupta, Department of Biological Engineering
___________________________________________________
Dr. Caixia Wan, Department of Biological Engineering
___________________________________________________
Dr. Azlin Mustapha, Department of Food Science
ACKNOWLEDGEMENTS
I would first like to thank Dr. Shramik Sengupta who has shown constant
support throughout my graduate school career, especially during rough personal
times. He has been extremely patient, and an excellent guide throughout this
whole process.
I would also like to thank my parents, Lori and Chris Colona, and my
fiancé, Emily Henderson, for their constant support throughout my studies.
Without them I would not be the person I am today, nor would I have been
capable of pursuing or completing this calling.
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TABLE OF CONTENTS
ACKNOWLEDGEMENTS ………………………………………………………...….. iii
LIST OF TABLES …………………………………………………………………....... vi
LIST OF FIGURES ……………………………………………………………………. vi
Chapter
1. INTRODUCTION ………………………………………………………………. 1
Motivation
Disc Diffusion
Agar Gradient Method
Broth-Dilution
Rapid Automated Susceptibility Systems
Phoenix Automated Microbiology System
Vitek 2
MicroScan WalkAway plus System
Polymerase Chain Reaction
Inoculum Effects
2. THEORETICAL BACKGROUND …………………………………………… 19
Introduction
Electrical Impedance Spectroscopy Previous Work
3. MATERIALS AND METHODS ……………………………………………… 29
Experimental Design
Sterilization
Antibiotics
Bacterial Cultures
Impedance Measurements
Analysis of Electrical Data
Statistical Analysis of Cb Trends
4. RESULTS AND DISCUSSION ……………………………………………… 42
iii
Escherichia coli + Ampicillin Results
Escherichia coli + Chloramphenicol Results
Pseudomonas aeruginosa + Gentamicin Results
Pseudomonas aeruginosa + Amikacin Results
Statistical Results
Conclusions
5. MODELING THE INOCULUM EFFECT ……………………………………. 65
Outline of Mathematical Model
Choice of Parameters
Solving the System of Coupled Ordinary Differential Equations
Modeling Results
Changing Bacterial Numbers
Other Parameters Effects on Inoculum Effect
6. FUTURE WORK ……………………………………………………………… 87
7. REFERENCES ……………………………………………………………….. 89
iv
LIST OF TABLES
Table
Page
2.1 …………………………………………………………………………...… 26
3.1 ……………………………………………………………………………... 40
4.1 ……………………………………………………………………………... 64
LIST OF FIGURES
Figure
Page
1.1. Disk Diffusion Test with Various Sized Zones of Inhibition ……………..… 2
1.2. Bacterial clearances created by E-test strips of two antimicrobials ……... 5
1.3. Microtiter plate with 96 wells with various antimicrobials listed as A-H …. 7
1.4. Phoenix Automated Microbiology System …………………………………. 9
1.5. Vitek 2 and AST Cards ………………………………………………………. 10
1.6. Clinical Process to obtain MIC ……………………………………………… 12
1.7. PCR Thermocycle Sequence ………………………………………...…….. 15
2.1. Microfluidic Design (a) and Equivalent Circuit (b) ………………………… 18
2.2. Bacteria-Antibiotic Combinations
with Various Antibiotic Concentrations ………………………………….. 25
3.1. Flow Diagram of Experimental Design …………………………………..… 29
3.2. Electrical Circuit Model for our Microfluidic Channel ……………………... 34
3.3. ZViewTM Equivalent Circuit Diagram ……………………………………….. 36
3.4. Bacterial Growth, Death, and Stasis vs Respective Cb Trends ………… 38
3.5. Problematic CPE-T graph …………………………………………………... 41
4.1. Escherichia coli + Ampicillin Results ……………………………………….. 42
v
4.2. Escherichia coli + Chloramphenicol Results ……………………………… 46
4.3. Pseudomonas aeruginosa + Gentamicin Results ………………………… 50
4.4. Pseudomonas aeruginosa + Amikacin Results …………………………… 54
4.5. Antibiotic Susceptibility Plots for Different Antibiotic-Bacteria Pairs ……. 60
4.6. RTM Generated Graph of Predicted and Actual CPE-T vs Time ………… 61
5.1. Diffusion across a thin membrane ………………………………………….. 65
5.2. Prolate Spheroid …………………………………………………………….. 68
5.3. 105 CFU/mL with (a) Control (b) 2 mg/l (c) 4 mg/l
(d) 8 mg/l (e) 16 mg/l (f) 128 mg/l antibiotic ……………………………. 75
5.4. 103 CFU/mL with (a) 2 mg/l (b) 4 mg/l (c) 8 mg/l
(d) 16 mg/l (e) 128mg/L antibiotic ………………………………………. 78
5.5. 108 CFU/mL with (a) 2 mg/l (b) 4 mg/l (c) 8 mg/l
(d) 16 mg/l (e) 128mg/L antibiotic ……………………………………….. 81
5.6. 108 CFU/mL with (a) 128 mg/L (b) 64 mg/L (c) 32 mg/L antibiotic …….. 84
5.7. 105 CFU/mL with (a) 1 mg/L (b) 0.5 mg/L antibiotic ……………………… 84
5.8. 103 CFU/mL with 0.5mg/L antibiotic ……………………………………….. 85
vi
Chapter 1: Introduction
Antibiotic Susceptibility Testing (AST) is used to determine what antibiotic will be
effective against a microorganism recovered from a clinical infection. There are two
common ways of performing AST: disc diffusion and broth dilution. The goal of
performing both kinds of tests is to determine the Minimum Inhibitory Concentration
(MIC) of a particular antimicrobial agent (antibiotic) against a particular bacterial strain.
MIC specifies the lowest concentration of antibiotic that will inhibit the growth of a
microorganism. This helps physicians determine what dosages of a particular antibiotic
will be effective.
Disc Diffusion – Disc diffusion is one of the oldest techniques used to determine a
microorganism’s susceptibility to an antimicrobial agent.
In this technique, a fresh culture of bacterial isolate is diluted until a McFarland standard
of 0.5 is reached using a photometric device. This optical standard represents a
concentration of 1-2x108 CFU/mL microorganisms in solution (Diseases 2013). After
reaching the desired concentration the suspension is spread evenly over a nutrient rich
plate. Mueller Hinton Agar is commonly used, but other agars are used for specific
bacterial isolates. Within 15 minutes of inoculation 6-12 disks are placed on the plates,
each containing a specific amount of antimicrobial. The plates are then incubated for
18-24 hours at 35oC, and checked for clearances created by the antimicrobial disks.
Depending on the concentration and microorganism’s susceptibility to the antimicrobial,
1
a clearing around the disks will form as seen in Figure 1.1 (Quizlet). The diameter of
these clearances are measured and interpreted using the Clinical and Laboratory
Standards Institute’s “Performance Standards for Antimicrobial Susceptibility Testing”
(CLSI 2007).
Figure 1.1 – Disk Diffusion test with various sized zones of inhibition (Quizlet)
These standards and the approximate clearance diameter can be used to obtain an
equivalent Minimum Inhibitory Concentration (MIC), and the microorganism will be
classified as susceptible, intermediately susceptible, or resistant to the antimicrobial
used (Diseases 2013). However, because of the approximation of inhibition diameter,
there can be resultant MIC error in this test. Automated diameter readers, such as the
OSIRIS video reader, have been produced to minimize this error and reduce manual
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labor involved in the process, but “variations of +/- 3 mm in zone size” were still
recorded using this method (Kolbert, Chegrani et al. 2004).
Thus, while this method is easy to perform, it is inherently qualitative. Another
drawback of this technique is that when there are many bacterial isolates and many
antimicrobials to be tested, a large number of agar plates must be prepared. This
requires a great deal of space and manual labor. Therefore for bacterial isolates that
have few antimicrobials associated with them, this test is great for generating a
qualitative assessment of antimicrobial susceptibility
Agar Gradient Method – A newer technique for determining antimicrobial
susceptibility known as an Epsilometer Test combines aspects of both dilution and
diffusion methods. In this method, a fresh bacterial isolate will once again be diluted to a
McFarland Standard of 0.5 using a photometric device, creating a solution concentration
of 1-2x108 CFU/mL. This solution is then inoculated onto a designated nutrient agar to
be incubated for a specific amount of time. Plates are once again generally incubated
for 18-24 hours, but can be longer depending on the species and should be verified by
CLSI standards (CLSI 2007). The “E-test” has a recommended list of media, such as
Mueller Hinton agar for aerobes and Brucella Blood for anaerobes (Microbiologia). In
this method, a strip of plastic has an antimicrobial gradient dried onto one of its
surfaces. The other surface of the strip has a scale of various concentrations written on
it, as well as an abbreviation of the antimicrobial that is dried on it. This strip is placed
onto the nutrient agar 15-20 minutes after inoculation with the antimicrobial gradient
facing down onto the agar’s surface. A zone of inhibition similar to the one seen in the
agar diffusion test will form around the strip, and can be seen in Figure 1.2
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(Microbiologia). As seen, the zone of inhibition becomes smaller as the antimicrobial
concentration decreases. The MIC can be determined by looking at where the zone
intersects with the plastic strip, and the concentration scale on the top side of the strip. If
the zone of inhibition is not clear cut and instead fades, the MIC can be read at the point
of complete clearance on the plate.
Like agar diffusion, this method is also very easy to interpret. However, 4-6
antimicrobial strips can be used on a 150mm plate at a time, reducing the time, space,
and manual labor necessary to test a range of concentrations of multiple antimicrobials
as compared to the agar diffusion method (BIODISK 2007). Additionally in a 2009 study,
Valdivieso-Garcia et al compared the E-tests and agar diffusion methods, and found
that “when all major laboratory components and labor were taken into account, the agar
dilution method was more costly (39.0% based on our costs)” (Valdivieso-garcía, R et
al. 2009). These reductions make this method a much better option than agar diffusion
when evaluating numerous antimicrobials. The ability to choose individual strips also
allows flexibility when choosing a panel of antimicrobials to test, making it more
convenient than broth-microdilution when testing specific antimicrobials.
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Figure 1.2 – Bacterial clearances created by E-test strips of two antimicrobials
(BIODISK 2007)
Broth-dilution – Broth dilution is a newer, but more commonly used test for
determining an antimicrobial’s MIC. It is also often used as a reference for emerging
methods, because of its reliability and ease of use (Document 2000). Test tubes of
liquid growth medium, commonly Mueller-Hinton Broth, are prepared with varying
concentrations of antimicrobial suspended in them. These concentrations generally
range from 0.5 – 128 µg/mL of antimicrobial, decreasing by a factor of two every test
tube. After preparation of these solutions, each test tube is inoculated with 5x10 5
CFU/mL of fresh pure culture of bacteria, and is incubated for a defined period of time
(18-24 hours) at 35oC. Test tubes are then evaluated for increased turbidity, which
5
indicates bacterial growth. The test tube containing the lowest concentration of
antimicrobial with no visible growth is considered the MIC.
To reduce the error associated with creating the correct concentrations of antibiotic
solutions, and reduce the time for setting up the test, microtiter plates containing 96
wells have been established. These trays contain frozen or dried antimicrobials in each
well (Schieven, Hussain et al. 1985). Each row contains a different antimicrobial while
each well within a row contains a different concentration of antimicrobial, once again
varying by a factor of two, as seen in Figure 1.3 (CDC). Each well is inoculated with
0.01 mL of solution containing a concentration of 5x105 CFU/mL isolated bacteria, and
incubated for a set period of time to allow bacterial growth. Wells are then examined by
visual inspection for increased turbidity or examined by automated readers, such as
Sensititre Autoreader, which measures fluorescence produced by bacterial enzymatic
activity on fluorogenic substrates (Staneck, Allen et al. 1985). Either of these methods
of examination produces an accurate MIC with reduced room for measurement error.
The microtiter trays that have been produced make this method very simple to use
when testing a larger amount of antimicrobials and receive a quantitative value for the
MIC, making them convenient for clinical laboratories. They have greatly reduced both
the manual labor and error associated with the preparation of standard broth dilution.
6
Figure 1.3 – Microtiter plate with 96 wells with various antimicrobials listed as A-H
(CDC)
Rapid Automated Susceptibility Systems – The use of automated systems
has grown tremendously since the first system known as Autobac 1 was introduced in
1974. In fact, in recent years it has been reported that, “approximately 83% of clinical
laboratories report using an automated instrument for primary susceptibility testing”
(Kuper, Boles et al. 2009). These systems come with premade antimicrobial
concentrations and can test a large number of isolates simultaneously. The automation
of these processes and ability to test a large number of isolates at once greatly reduces
the amount of manual labor that would normally be required to set up and run AST.
Additionally, automated systems will use methods with heightened sensitivity to
automatically determine the MIC of antimicrobials, which reduces the time taken to
7
determine susceptibility and can result in earlier administration of targeted antimicrobial
therapy.
One downside to automated systems is that they are generally very costly
initially. These costs are said to be overcome by the reduction in manual labor required
for standard methods, a reduction in inpatient time, and a reduction of surgical
procedures (Sellenriek, Holmes et al. 2005). Another flaw of these systems is that
additional manual tests must still be done completed for certain species and some
antimicrobial resistant organisms, lessening these systems’ overall effectiveness.
Finally, these systems cannot decipher between bacteriostatic, and bactericidal
antimicrobial mode of action. Reviewed are three common automated systems used for
antimicrobial susceptibility testing.
Phoenix Automated Microbiology System: The BD PhoenixTM Automated
Microbiology System is capable of both identifying bacterial species as well as testing
them for antimicrobial susceptibility. Microorganisms must first initially be diluted to a
McFarland Standard of 0.5, and then 0.25 μL of the solution is added to a Phoenix AST
broth, creating a final concentration of ~5x105 CFU/mL of bacterial isolate. The system
then uses a redox dye contained in the AST broth in combination with kinetic
measurements of turbidity to measure bacterial growth. It uses a computer algorithm to
analyze these measurements after inoculation and compares resultant MIC’s with
standardized values every 20 minutes (Wiles, Turner et al. 1999). This allows for a
shortened time to result of susceptibility, which showed an average between ~9-14 hrs
when tested with Enterobacteriaceae spp., Staphylococcus spp., Enterococcus spp.,
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and various nonfermenting spp. (Eigner, Schmid et al. 2005). This device can be seen
in Figure 1.4.
Figure 1.4 - Phoenix Automated Microbiology System (BD)
VITEK 2: The VITEK 2 system is also capable of both identifying bacterial
species as well as testing them for antimicrobial susceptibility. Plastic cards within the
system contain 64 micro-channels filled with antimicrobials or biochemical substrates
and growth media, as seen in Figure 1.5. Initially, a test tube containing the
microorganism is placed into a vacuuming system, which disperses the suspension into
each of the micro-channels. An optical system measures the turbidity and colored
substrates in micro-channels every 15 minutes to evaluate the susceptibility to the
antimicrobial present in each micro-channel (Pincus).The average time to result of
susceptibility has been reported at ~6-12 hours when tested with Enterobacteriaceae
spp., Staphylococcus spp., Enterococcus spp., and various nonfermenting spp. (Eigner,
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Schmid et al. 2005). Various sized and levels of automated versions of this system have
been created to accommodate the varying volume of tests required by different clinical
laboratories, such as the VITEK 2 Compact for smaller laboratories, and the VITEK 2
XL with large capacities and greater automation for larger laboratories (Pincus).
Figure 1.5 - VITEK 2 and AST cards (Biomerieux)
MicroScan WalkAway plus System: The MicroScan WalkAway plus System is
another system that can perform both identification and susceptibility tests for a
microorganism. It utilizes a microdilution method for its automated tests, and has two
different size systems that can store either 40 or 96 microdilution trays depending on
laboratory needs. The microdilution trays must be inoculated manually with ~5x105
CFU/mL of bacteria, using the same procedures as previous methods. It then utilizes
fluorometic biochemical reactions and photometric readings to measure bacterial
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growth. These measurements are then interpreted by the system’s software to provide
exact MIC endpoints, claiming to not need historical data for its interpretations. During a
comparative study of the WalkAway and with the VITEK AutoMicrobic System
performed by M.A Pfaller et al., the average time for the determination of susceptibility
of gram-negative bacteria was reported as 3.5-7 hours(Pfaller, Sahm et al. 1991).
Additionally, when gram-positive bacteria were tested, the time to determine
susceptibility was reported as 3.5-15hrs (Bascomb, Godsey et al. 1991 ). This system
offers special overnight automation features for problematic microorganisms or cultures
incubated late in the day.
Automated tests have become the most prominently used method for
determining susceptibility in clinical laboratories due to their ability to rapidly test large
quantities of microorganisms and antimicrobials. All three automated systems tested
extensively against disk and broth macrodilution methods to show they can accurately
provide susceptibility results for the organism-antimicrobial combinations they claim
(Sellenriek, Holmes et al. 2005). Additionally, they have all been compared against one
another with varying susceptibility time results based on the organisms tested in the
study. When comparing a wide array of both gram-negative AND gram-positive, the
VITEK 2 system had the quickest average time to determining susceptibility at 9 hours,
while the MicroScan system had the slowest average time at 20 hours (Sellenriek,
Holmes et al. 2005). These accelerated results are also only beneficial when there is
staff available to receive the results and then take the required actions based on the
results, diminishing their value somewhat in understaffed and laboratories with limited
hours. Because of this and other various reasons, some laboratories still choose to only
11
use manual methods for susceptibility testing. Manual methods are also still commonly
used in conjunction with automated systems for cases where automated systems
cannot determine susceptibility. Finally, manual methods also serve as a reference for
emerging and existing technologies.
The most important drawback lies in the long amount of time required to set up
an AST, and hence obtain the MIC value. This time delay is very important as the time it
takes to administer targeted antibiotics has been linked to patient outcomes in severe
infections such as sepsis (Gaieski, Mikkelsen et al. 2010).
Figure 1.6 – Clinical Process to obtain MIC (Workflow)
As shown in Figure 1.6, in order to set up a standard clinical AST, an infected
sample must first be streaked onto some type of agar media. The agar is then placed in
an incubator for (12-36 hours), until individual colonies have formed. Colonies are then
isolated and placed into a given solution. This solution is then tested turbidometrically
and is set to a McFarland Standard of 0.5. Finally, these solutions are then placed into
12
an automated reader, which will determine MIC. The streaking of the infected sample,
its overnight incubation, and preparation of the turbidometric standard solutions from
individual colonies contribute to a large time (often > 36 hrs) before the MIC values
become available to the clinician. In addition, since performing these procedures
requires scheduled skilled manual labor (and clinical microbiology labs often have a
limited number of skilled personnel), one or more of these processes may be performed
only at certain times of the day, causing more time to be lost in the process.
Secondly, since absence of visible growth is the only indicator of inhibition in this
method, one cannot decipher whether the antimicrobial has killed the microorganisms
(bactericidal) or has merely prevented the growth of the microorganisms (bacteriostatic)
without further testing of the solutions, such as calorimeter assay, which can take up to
one additional day. Some infections require specifically bacteriostatic or bactericidal
antimicrobial effects. This makes it extremely pertinent to understand the effect that an
antimicrobial has on an unknown microorganism, as antimicrobials can have varying
effects on different species and on different subspecies. For example, Pneumococcal
Meningitis is susceptible to multiple antimicrobials, but it is imperative for bactericidal
effects to be achieved to clear the infection (Scheld and Sande 1983). Therefore, from
standard AST results alone, it may not be evident which antimicrobial should be
administered to combat Pneumococcal Meningitis. On the other hand, some cases of
streptococcal and clostridial gangrene requires bacteriostatic agents for optimal
treatment. This is because bacteriostatic agents inhibit the production of deadly toxins
the bacteria produce, while bactericidal agents may cause these toxins to be released
from the bacteria into the surrounding environment (Finberg, Moellering et al. 2004).
13
Thus there is a need for technologies that can not only cut down the time needed
to determine MIC values, but also provide additional information (such as the mode of
action of the antibiotic on the bacteria). Although there are a number of emerging
technologies in the area of Antibiotic Susceptibility Testing in general, they are unable to
provide these pieces of information.
Polymerase Chain Reaction (PCR) - For instance, PCR is being explored.
Short sequences of known DNA, known as primers, are added to a solution containing
DNA to be tested. The temperature of the mixture is then raised to 94 °C at which
denaturation of the tested DNA occurs. The temperature of solution is then lowered to
55-60 °C, which allows primers to anneal to their complimentary denatured single
stranded DNA sequences. The temperature is then raised to 72°C, which is the proper
temperature for Taq polymerase to attach to primer sequences, and synthesizes a
complementary strand to the targeted DNA sequence in a 5’ to 3’ direction. The
substrate is then cleared. After three cycles, a full sequence containing both the forward
primer, reverse primer, and all base pairs in between will be created. This cycle can
then be repeated many times over to produce millions of desired sequences.
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Figure 1.7 - PCR thermocycle sequence (PCRWiki 2015)
To test for antibiotic resistance, bacterial isolates are lysed and DNA is extracted
using premade kits such as DNeasy tissue kit (Strommenger, Kettlitz et al. 2003).
Primers of sequences known to be associated with a particular antibiotic resistance,
such as mecA (oxacillin), tetK (tetracycline), and blaZ (penicillin) resistance genes, are
then added to the DNA solution (Strommenger, Kettlitz et al. 2003). The PCR
thermocycle sequence depicted in Figure 1.7 is then carried out. If the DNA contains the
complimentary sequence to the primer it will be amplified, if it does not, it will not be
amplified. Amplified DNA sequences can then be analyzed using agarose gel
electrophoresis to check for correct fragment size, or can compared to published
sequence data using software such as DNASTAR (Strommenger, Kettlitz et al. 2003).
15
This technique provides results for antibiotic susceptibility in 6 hours or less,
making it potentially faster than current automated systems. However, testing for a
resistance gene once will only qualitatively determine if the organism is resistant or
susceptible to an antibiotic. It will not yield an MIC or demonstrate the effect the
antibiotic will have on the organism present. Quantitative PCR (qPCR) tests can be
used over several hours to measure the growth kinetics; however, running several PCR
tests per antibiotic is currently very costly making it a poor choice for clinical use
(Rolain, Mallet et al. 2004). In addition to these drawbacks, analysis of PCR results is
limited to well-known pathogens and resistance genes. This could be an issue when
testing bacteria from varying environments or locations, as bacterial species and the
manner in which they achieved antibiotic resistance may be different in different parts of
the world. For example, when testing 216 samples of Acinetobacter baumanii only 111
had DNA identical or very similar to the A. baumanii species being tested for (Ecker,
Massire et al. 2006). This means nearly 50% of samples would not show the proper
results, using their PCR method.
PCR offers a new quick way of determining antibiotic susceptibility, but suffers
from either only being able to qualitatively assess antibiotic susceptibility or being very
costly when using (qPCR), In addition it is limited to well-studied pathogens and genes.
Even the MIC as currently measured is sometimes not sufficient to guide the
clinician to a “correct” dose of antibiotic. This is because the MIC determined in-vitro is
for a standard bacterial load of 105 CFU/ml. In contrast the actual load present in-vivo
varies with the type of infection: septicemia can present with 10-100 CFU/ml, orthopedic
infections with 105 CFU/ml, and Meningitis with 107 or more CFU/ml.
16
Although it may be intuitively expected that apparent MICs would change with
bacterial loads (with higher bacterial loads requiring larger amounts of antibiotic), in
practice, there is a wide variation in the effects seen on MICs – and the reasons for the
variation are not very well understood. For instance, in Pseudomonas aeruginosa it was
shown that using initial concentrations of 105, 107, 108 organisms per ml had various
effects on the bactericidal activity of ten beta-lactams antibiotics. In some antibiotics,
such as Azlocillin, MIC values rose from 4 µg/ml to >500 µg/ml, while in others, such as
Gentamicin, MIC values only rose from 2 µg/ml to 4 µg/ml (Eng, Smith et al. 1984). In
Escherichia coli (ATCC strain 25922), amoxicillin, amoxycillin–clavulanate combination,
piperacillin, and piperacillin–tazobactam combinations were all compared using both
broth microdilution and agar diffusion method with standard concentrations and 100 fold
higher bacterial concentrations. Piperacillin, and piperacillin–tazobactam combinations
showed very large increases in MIC from 2 µg/ml up to 256 µg/ml, while amoxycillin and
Amoxycillin–clavulanate combinations showed no increase in MIC at differing bacterial
concentrations (Lopez-Cerero, Pico et al. 2009).
Additionally, it is important to understand what type of antimicrobial effects an
antibiotic will have at lower initial bacterial concentrations, as it has been shown that
various initial concentrations of bacteria can have an effect on antibiotics antimicrobial
effectiveness (LaPlante and Rybak 2004).
Additionally, it has been shown that the antimicrobial effects of an antibiotic can
change due to inoculum size. In Staphyloccocus aureus MICs were found for nafcillin,
vancomycin, daptomycin, and linezolid at ~5x105 CFU/ml and at ~1x109 CFU/ml.
17
Vancomycin, and nafcillin were both able to achieve bactericidal activity at standard
bacterial concentration, but were unable to achieve bactericidal activity at ~1x10 9
CFU/ml (LaPlante and Rybak 2004).
While there do exist studies like those mentioned above looking at high bacterial
loads, there are very few studies which investigate what the effects on MIC and action
of antibiotics at lower bacterial loads. We suspect that this is due to the absence of
automated technologies that can monitor the growth and/or the death of bacteria when
their concentrations in suspension are ~ 103 CFU/ml, or lower. Since a number of
important diseases, such as septicemia, in-vivo bacterial loads are at these low values,
studying the antimicrobial effect of antibiotics on various microorganisms at lower loads
may yield clinically valuable information. In this study we will investigate the use of
Electrical Impedance Spectroscopy (multi-frequency impedance measurements) to
determine MIC and antibiotic action at low bacterial loads (~ 103 CFU/ml).
18
Chapter 2: Theoretical Background
Electrical Impedance Spectroscopy: When an alternating (AC) voltage is applied to a
material, an AC current passes through it. This magnitude of the current is typically
proportional to the magnitude of the voltage applied. In addition, the phase of the
current may differ from the phase of the applied voltage. Electrical impedance is a
quantity that describes the manner in which a material resists the flow of AC current
through it as a result of the applied AC voltage. It is comprised of two parts: an in-phase
(with the voltage) part known as resistance (R) and an out of phase part known as the
reactance (X). It is customary to represent the impedance (resistance and reactance) as
a complex number, as shown in Equation 2.1.
2.1)
Z  R  jX
Where j 
1
X can be further split into two parts, capacitance reactance (Xc) and inductive reactance
(XL) at a given frequency (f). These parts can be described by Equations 2.2 and 2.3.
Where C is capacitance, and L is inductance.
1
2.2)
𝑋𝐶 = − 2𝜋𝑓𝐶
2.3)
𝑋𝐿 = 2𝜋𝑓𝐿
The physical contents of a medium dictate its impedance. In a biological solution
for example, whole cells, proteins, lipids, and even ions within the solution all contribute
19
to the solutions impedance. Thus when any of these physical contents change, the
impedance of the solution will change as well.
Sengupta et al. have previously developed an approach to determine if viable
bacterial were present in a solution. Bacteria are capable of storing up to ~100x the
charge of an equal volume of water (Poortinga, Bos et al. 1999). This is due to the fact
that bacterial cell membranes act as a semi-permeable membrane, which regulates the
flux of charged and hydrophilic molecules in and out of the cell to maintain osmotic
balance. Typically, there will be an unequal concentration of charged molecules outside
and inside due osmotic balancing causing just outside of the cell membrane to be
slightly positively charged with respect to the inside of the cell membrane. This unequal
distribution of charge between sides of the cellular membrane will cause oppositely
charged ions to accumulate on each side of the cell membrane. The resistance of flow
ions and accumulation of ions results in the bacteria behaving like a capacitor
(Puttaswamy, Lee et al. 2011).
Based on this behavior, Segupta et al. explained that an increase in the number
of bacteria would result in a measureable increase in the charge storing capacity
(capacitance) of the medium; thus resulting in an increase in the reactance of the
solution (Sengupta, Battigelli et al. 2006). This idea had been proposed previously, but
no one was able to detect significant changes in reactance due to bacterial proliferation
(Felice and Valentinuzzi 1999). Sengupta et al. showed that this was due to a couple of
reasons. The AC signal frequencies used previously were too low, and the previous
geometry of the measuring system caused the electrochemical interface between the
electrodes and the aqueous solution (surface capacitance) to effectively “screen” the
20
capacitance due to the biological sources in the solution (bulk capacitance)
(Puttaswamy, Lee et al. 2011). To remedy these issues, they built a long-narrow
microchannel with gold electrodes at each end of the channel as shown in Figure 2.1a.
Biological solution would fill the microchannel, and then impedance measurements
across the system would be taken at multiple frequencies including frequencies higher
than previously used (up to 1MHz). Increasing the length of the channels and
minimizing its width, increased the significance of the capacitance contributed by the
biological sources within the solution. An equivalent circuit model was then developed to
describe the physical characteristics of this channel shown in Figure 2.1b. This model
was then used with impedance measurements at multiple to differentiate the surface
capacitance from the bulk capacitance. In addition, AC frequencies that were higher
than previously tested were used to help reduce the “screening” effect caused by the
electrochemical interface. Using impedance measurements at various frequencies with
these new described developments, Sengupta et al. were then able to detect bacterial
proliferation in Tryptic Soy Broth (TSB) with an initial load of ~100 CFU/mL of E. coli in
approximately 3 hours (Sengupta, Battigelli et al. 2006). However, this original method
was very temperature sensitive, and did not reach a high enough frequency to negate
all of the “screening” effect caused by low frequencies. This study proposed that a
system consisting of an aqueous solution in a microfluidic channel with electrodes on
either end shown in Figure 2.1a could be used to measure these increases. This system
could then represented by an equivalent electrical circuit as shown in Figure 2.1b.
21
Figure 2.1 - Microfluidic design (a) and equivalent circuit (b) (Puttaswamy 2013)
In 2010, Puttaswamy et al. was able to increase this methods sensitivity, and
proved it could be used in a real world setting. In this study, the sensitivity of the system
was increased by increasing the frequency range at which impedance measurements
were taken up to 100 MH, and a newer refined electrical model was developed. This
model along with more rigorous data analysis was able to describe the behavior of the
22
bacterial particles at high frequencies and differentiate changes in reactance due to
bacterial proliferation and temperature fluctuations (Puttaswamy, Lee et al. 2011).
With this more reliable system, this technique was tested using more “real world”
fluid samples. First it was used to detect microorganisms in food substrates, such as
milk and apple juice. Using this method, ~ 1, 10, 100, and 1000 CFU/ml of E. coli in milk
was detected in approximately 4.5, 3, 2, and 0.5 hours, respectively. For the same initial
loads, Lactobacillus was detected in apple juice are approximately 8, 6, 4, and 1 hours
(Puttaswamy 2013).This method was then used for Blood Culture (a test to detect the
presence of live bacteria in human blood, wherein 2-10ml of the blood is added to ~3040ml of bacterial growth media, and the resulting “blood culture broth” is monitored for
the presence of living microorganisms). In this case, our method was bench-marked
against the BACTECTM (a commonly used blood culture system marketed by Becton
Dickinson that detects the presence of microorganisms in blood cultures via a change in
the CO2 levels in the fluid brought about by microbial metabolism). In this study, our
method was able to detect ~1,~10,~100, and ~1000 CFU/ml of E. coli in blood in 4, 3, 2,
and 1 hour, respectively. For BACTECTM, the corresponding times to detection (TTDs)
were approximately 16, 12, 10, and 8 hours, respectively (Puttaswamy, Lee et al. 2011).
We were able to achieve these shorter TTDs because our threshold concentration (the
bacterial load reached by the proliferating bacteria at which we are able to discern a
difference from the background) was ~ 1000 CFU/ml. In contrast, the threshold
concentrations for BACTEC (and other commercially available continuously monitored
blood culture systems) is ~ 1x108 CFU/ml (Smith, Serebrennikova et al. 2008).
23
Another clinical application that was explored for this technique was in
performing Antibiotic Susceptibility Testing (AST). This application relies on the fact that
while bacteria have the ability to become polarized and store charge when alive, they
lose this ability as their membrane potential drops upon damage to cells (ultimately
going to zero upon cell death) (Kirchman, Giorgio et al. 2008). Thus, while a bacterial
population that continues to grow in the presence of antibiotic should display a signal
similar to the prior applications (viz. an increase in bulk capacitance of the suspension
(Cb) over time), a bacterial population that is dying off should display an opposite effect:
viz. the Cb will decrease over time. Moreover, a bacterial population that remains
steady should have its Cb remain at a steady value over time.
Puttaswamy et al. (Puttaswamy, Lee et al. 2012) demonstrated the use of this
approach on “standard” (5x105 CFU/ml) suspensions of three well-characterized
bacterial strains (Escherichia coli ATCC 25922, Staphylococcus aureus ATCC 29213,
Pseudomonas aeruginosa ATCC 27853), each against two different antibiotics. In this
work, 1x106 CFU/mL bacterial suspensions were added to equal volumes solutions
containing various concentrations of antibiotics to yield suspensions containing 5x10 5
CFU/ml of the bacteria, and (depending on the solution), 0.5-128 mg/L of the antibiotic
of interest (with the antibiotic concentration increasing in a twofold manner). Impedance
measurements were taken immediately after mixing the bacterial suspensions and the
antibiotic solutions, and every hour thereafter for 4 hours following the initial
measurement. Bulk Capacitance (Cb) was calculated from each impedance
measurement, and plotted as a function of time. Selected results are shown in Figure
2.2.
24
Figure 2.2 - Bacteria-Antibiotic Combinations with Various Antibiotic
Concentrations (Puttaswamy, Lee et al. 2012)
25
As seen in Figure 2.2, for controls (suspensions with no antibiotic), Cb values
increased monotonically (positive slope). However, with increasing concentrations of
antibiotic, these lines plotting the values of Cb over time either went flat (zero slope) or
showed a negative slope (decrease in Cb over time). The lowest concentration of
antibiotic which did not show a significant increase in bulk capacitance over time was
deemed to be the Minimum Inhibitory Concentration (MIC). As Shown in Table 2.1 the
values of MIC obtained using this method were in agreement with previous studies as
(Puttaswamy, Lee et al. 2012).
Table 2.1 - MIC value comparison of this method vs Standard values
(Puttaswamy, Lee et al. 2012)
26
In addition to providing accurate MIC results, this method was also able to
distinguish actions of a bacteriostatic antibiotic (like Chloramphenicol for E. Coli,
Chloramphenicol for S. aureus, and Amikacin for P. aeruginosa) from those of
bactericidal ones (like Ampicillin for E. Coli, Gentamicin for S. aureus, and Ampicillin for
P. aeruginosa). As expected, with bacteriostatic antibiotics at concentrations ≥ MIC, we
observed the value to Cb to remain unchanged, whereas for bactericidal antibiotics at
concentrations ≥MIC, values of Cb decreased over time. Conventional broth dilution
studies using optical readers are unable to distinguish the effects of bactericidal and
bacteriostatic antibiotics, and hence an additional test (taking > 1 day) is usually needed
to evaluate this. Our method thus provides information over and beyond that provided
by a standard broth dilution MIC assay.
Also, given the fact that our “threshold” loads are ~ 1000 CFU/ml (meaning that
we should be able to electrically discern a difference between suspensions containing ~
1000 CFU/ml from suspensions containing no living micro-organisms), and thus our
method should allow us to “observe” in real-time the interaction between
microorganisms present at low loads in suspensions and antibiotics at concentrations of
interest.
While such studies are of potential use given that antibiotics often interact with
microbes present at low loads in vivo (as in the case of bloodstream infections), very
few such studies have been performed in the past, most-likely due to the time and effort
such a study would otherwise entail. In this piece of work, we demonstrate the ability of
our electrical method to meet these goals: viz. to determine within 4 hrs, the effect of
27
various concentrations of antibiotics of interest against low loads of bacteria (~ 1000
CFU/ml), and to thereby record “effective” MICs for bacterial loads of clinical interest.
28
Chapter 3: Materials and Methods
Experimental DesignThe overall design of our experiment is depicted in Figure 3.1 below.
In brief: ATCC isolates of well-characterized bacteria (Escherichia coli ATCC
25922 and Pseudomonas aeruginosa ATCC 27853) were incubated to obtain cultures
with bacterial concentrations ~1x108 CFU/mL. The bacterial solutions were then serial
diluted in Mueller-Hinton Broth (MHB) to reduce the bacterial concentration in solution to
~104 CFU/ml. Separately, concentrated stock solutions of candidate antibiotics to be
tested were created, also in MHB. Appropriate amounts of antibiotic stock solution in
MHB, and MHB were added to the bacterial suspension containing ~10 4 CFU/ml of
bacteria to create a suspension containing ~ 103 CFU/ml of bacteria of interest and the
candidate antibiotic at the target concentration. These suspensions were then incubated
at 37C for a period of 4 hours.
Immediately after the creating of these solutions and every hour thereafter, test
tubes containing the bacteria-antibiotic mixture were removed from the incubator and
two parallel aliquots drawn from them. 100 µL of the solution would be appropriately
diluted and plated onto MH agar. In addition, 35 µl of the solution would be inserted into
a microfluidic cassette, and the sample in the cassette was assayed electrically to
obtain the impedance (Z) over a range of frequencies () ranging from 1 KHz to
100MHz. The electrical scan data (Z vs. w) was analyzed offline to obtain an estimate of
the bulk capacitance (Cb) of the solution at the time of the electrical scan. The Cb
values of any given suspension over a period of 0-4 hrs (5 readings) was then plotted
against time, and statistically evaluated to determine if the Cb values were increasing,
29
decreasing or static over time. The lowest concentration of antibiotic for which
statistically significant growth did not occur was deemed to be the Minimum Inhibitory
Concentration for that antibiotic-bacteria pair.
Figure 3.1 – Flow Diagram of Experimental Design
Details of the various steps are provided below.
Sterilization All media used throughout the experiment and materials used in the experiment,
besides the microfluidic cassettes, were autoclaved at 121oC for one hour and then
placed in biosafety hood to ensure sterility. Double DI water was inserted into
30
microfluidic channels and was allowed to sit in the channels for 5 minutes. The DI water
was then pushed out of the channels with a sterile micropipette. 70% ethanol was then
inserted into the channel, which was allowed to sit for 10 minutes. Ethanol was pushed
out of the channel, and double di water was inserted back into the channels for 5 more
minutes. DI water was flushed from the channels once again, and the entire microfluidic
cassette was then placed into a 70% ethanol bath for 30 minutes. Finally, the channels
were rinsed with double DI water multiple times, and were placed in a sterile fume hood
under UV until execution of an experiment.
Antibiotics –
Ampicillin and Chloramphenicol were tested against E. coli, and Gentamicin and
Amikacin were tested against P. aeruginosa. These antibiotic-bacterial pairs were
chosen because they had been tested previously in many AST studies using standard
testing methods, as well as tested using impedance spectroscopy at 10 5 CFU/mL (Eng,
Smith et al. 1984, Lopez-Cerero, Pico et al. 2009, Puttaswamy 2013). Therefore, a
proper comparison between MIC and antimicrobial effect at various bacterial loads
could be made. Additionally, at 105 CFU/mL one antibiotic per organism had shown
bactericidal effects (Ampicillin for E. coli and Gentamicin for P. aeruginosa), while the
other antibiotic had shown bacteriostatic effects (Chloramphenicol for E. coli and
Amikacin for P. aeruginosa) against their respective organisms when tested using both
standard testing methods and when using our method. A concentration range of 0.5-128
mg/L was used for each antibiotic with each step increasing by a factor of two
(Document 2000).
31
Bacterial Cultures Escherichia coli (ATCC 25922) and Pseudomonas aeruginosa (ATCC 27853)
were chosen as they have been commonly studied in AST studies with various
antibiotics (Eng, Smith et al. 1984, Lopez-Cerero, Pico et al. 2009, Puttaswamy, Lee et
al. 2012). E. coli was incubated at 37oC for 12-16 hours, while P. aeruginosa was
incubated for 18-24 hours in Mueller-Hinton Broth (MHB) to obtain cultures >1x108
CFU/mL.
Sample Preparation –
After incubating cultures for the specified amount of time, solutions would be
inserted into an optical density (OD) tube, one OD tube containing MHB for use as a
control, and one containing a dilution of the culture in MHB. Using a UV-Vis
spectrophotometer, cultures were diluted appropriately until reaching an OD of .1-.15
OD, which would yield a solution containing a bacterial concentration ~1x10 8 CFU/ml
(Fass and Barnishan 1979). The bacterial solutions were then serial diluted using
Mueller-Hinton Broth (MHB) to reduce the bacterial concentration in solution to ~10 4
CFU/ml. 0.0256g of the desired antibiotic was added to 10 ml of MHB. This solution
(~2560mg/L) was then diluted down to twice the desired antibiotic concentration to be
tested (1, 2, 4, 8, 16, 32, 64, 128, 256 mg/L). 2.5 mL of each solution was then added to
1.5ml of sterile MHB, and 1 mL of bacterial solution (1x104 CFU/ml). This would yield a
total of 5 mL of solution containing a bacterial concentration of ~2x103 CFU/ml and an
32
antibiotic concentration that is half of the initial preparation (.5, 1, 2, 4, 8, 16, 32, 64, 128
mg/L). Cultures were then incubated at 37oC for four hours following inoculation.
Impedance Measurements
Immediately after bacterial inoculation into the antibiotic solutions and every hour
after inoculation, test tubes containing the culture-antibiotic mixture would be removed
from the incubator, and 200 µl would be drawn from the solutions into a sterile
Eppendorf tube. The solution would then sit for 10 minutes to allow it to reach room
temperature. 100 µl of the solution drawn was then diluted appropriately (estimated by
expected kill/growth curves), and plated onto MH agar. Diluting the solutions before
plating them onto MH agar was done to ensure that a countable number of bacterial
colonies (~20-100) was present on the plates, and would provide a bacterial
concentration vs time reference for our bulk capacitance vs time readings. After 10
minutes had surpassed, 35 µl of the solution drawn was also inserted into a microfluidic
cassette. This process was carried out for every antibiotic concentration as well as for a
control for each organism.
The microfluidic cassette contains two gold electrodes at the ends of a
microfluidic channel. Each electrode is connected to an Agilent 4294A Impedance
Analyzer, and electrical impedance measurements were taken over at 200 frequencies
(ω) ranging from 1 kHz to 100 MHz. At each designated frequency, a 500mV voltage is
generated, and the magnitude and phase of the AC current across the microfluidic
channel is recorded. The ratio of applied voltage and the recorded current (along with
the phase-difference between these two quantities) is used to calculate the Impedance
33
(Z). Impedance is usually represented as a complex number consisting of a “real” part
called Resistance (R) that is in-phase with the voltage and an “imaginary” part called
Reactance (X) that is 90o out-of-phase with the applied voltage. Mathematically,
3.1)
𝑍 = 𝑅 + 𝑗𝑋
Where j 
1
Therefore, |𝑍 | = √𝑅 2 + 𝑋 2
𝑋
𝜃 = tan−1 𝑅
Analysis of Electrical Data
A circuit model has been constructed previously to model our microfluidic
device’s various physical attributes such as, electrode resistance (Re), capacitance at
the electrode-solution interface (Ce), bulk-solution resistance (Rb), and capacitance of
the bulk-solution (Cb) as seen in Figure 3.2 (Puttaswamy 2013). This model allows us to
differentiate resistance and capacitance changes due to bacterial proliferation or death
in the bulk of the solution from changes that may occur at the electrode’s interfaces. C e
is approximately 103 times larger than Cb, so percentage deviations at the electrode
interface would outweigh capacitance increases or decreases contributed by C b if these
capacitances were calculated together, and were not separated into individual
components.
34
Figure 3.2 – Electrical Circuit Model for our Microfluidic Channel (Puttaswamy 2013)
To obtain values for this electrical circuit models a modeling software named
ZViewTM fits measured R and X data from the impedance analyzer to a similar circuit
model. In the programs model, we replaced the capacitors in the circuit above by
Constant Phase Elements (CPEs) or non-ideal capacitors. In an ideal capacitor,
charges accumulate instantly. However, at both the electrodes and at bacterial cell
membranes, it takes a finite amount of time for charges (ions) to accumulate, and this
behavior is better modeled as a CPE. While capacitors impedance is described by
Equation 3.2, constant phase elements can described by Equation 3.3. In Equation 3.3,
n can range from 0-1, and is representative of the Phase-Angle of CPE (CPE-P). When
n is equal to 1 in this equation, it is identical to the capacitor impedance equation.
3.2)
𝑗
𝑍 = − 2𝜋𝑓𝐶
35
3.3)
𝑗
𝑍 = − (2𝜋𝑓𝐶)𝑛
The use of CPEs in our model provides a close fit to impedance data, as can be
seen in Figure 3.3, where the blue data points (and the red line) are the actual data, and
the green line is the curve of best fit obtained for the parameter values shown in the
inset box.
36
Figure 3.3 – ZViewTM equivalent circuit diagram with Constant Phase Elements, as well
as R vs X data with Impedance Analyzer measured data (blue line) aligned with
expected data from fitted circuit model values (green line).
For every impedance recording taken an R vs X plot is acquired, such as in
Figure 3.3. Values for each parameter in the circuit are also then acquired through
ZViewTM. The magnitude of the CPE of the bulk (CPE2-T) is representative of how
much charge is stored within the solution at the membranes of living bacteria. This
element is the main focus of our measurements, and its trends were monitored over a
four hour time course to determine whether bacteria is proliferating, dieing, or remaining
static. All of these trends as well as bacterial numbers can be seen in Figure 3.4. As
seen in the figure, bulk capacitance (CPE2-T) values vary in concert with plate counts of
aliquots taken at the same time as the electrical scans.
37
Bacterial Death
1.30E-11
6.00E+03
5.00E+03
CPE2-T
1.20E-11
CPE2-T
4.00E+03
1.10E-11
3.00E+03
1.00E-11
Plate
Count
2.00E+03
9.00E-12
1.00E+03
8.00E-12
0.00E+00
0
1
2
3
4
Time (hrs)
Bacterial Stasis
7.5E-12
1.00E+05
7.45E-12
1.00E+03
7.3E-12
1.00E+02
7.25E-12
1.00E+01
7.2E-12
7.15E-12
1.00E+00
0
1
2
Time (hrs)
3
4
Bacterial Growth
1.15E-11
1.00E+05
CPE2-T
1.10E-11
1.05E-11
1.00E+04
Plate Count
CPE2-T
7.35E-12
Plate Count
1.00E+04
7.4E-12
1.00E-11
9.50E-12
1.00E+03
0
1
2
Time (hrs)
3
4
Figure 3.4 - Bacterial Growth, Death, and Stasis vs Respective Cb Trends
38
Statistical analysis of Cb trends
In addition to preliminary visual inspection of CPE2-T’s trend over time, a
statistical model was developed to assess trends of bulk capacitance values with
greater certainty. In this model, it is assumed that two parts contribute to the C b value
obtained by ZViewTM. Various proteins and ions within the solution in which bacteria are
suspended cause the solution to store some charge. Thus, the first part of the bulk
capacitance is the capacitance contributed by the solution (Cb_soln) in which bacteria are
suspended. As explained previously, viable bacteria accumulate charge at their
membrane and act as a capacitor in an AC electric field. Accordingly, the second part of
the bulk capacitance is the capacitance contributed by individual bacterial cells (C b_bac).
This part is multiplied by the number of viable bacteria in solution (n) to provide the net
contribution by bacteria. The sum of these two parts makes up the total bulk
capacitance, as can be seen in Equation 3.2.
3.2)
CPE2-T = Cb_soln+(n*Cb_bac)
Additionally, the number of viable bacteria (n) in the solution is expressed by equation
3.3 for bacteria, until the bacteria has reached a stationary phase. In this equation, n o is
the initial number of bacteria in solution, k is a specific growth/death rate, and t is the
time over which measurements are taken.
3.3)
n = no*ekt
39
Thus if CPE2-T values over time are fit to these two equations, bacteria
proliferating over time should produce a positive k value, bacteria dieing over time
should produce a negative k value, and for bacterial numbers remaining constant over
time k should be virtually zero. Using the software RTM, data series were fit to the model
in Equation 3.2. This software also performed a P-test on each data set to assess
whether k was statistically equivalent to zero or not. The conclusions drawn (increasing,
decreasing, or static CPE-T) from k and P value combinations obtained from this model
can be seen in Table 3.1.
P ≤ 0.90
P ≥ 0.90
(+) k value
Increasing CPE-T
Static CPE-T
(-) k value
Decreasing CPE-T
Static CPE-T
Table 3.1 – Conclusions drawn from k and P value combinations
This model was especially vital for data sets that had unclear trends, such as in Figure
3.5.
40
CPE-T vs Time
1.12E-11
1.10E-11
CPE-T
1.08E-11
CPE-T
1.06E-11
1.04E-11
1.02E-11
0
1
2
3
Time (hrs)
Figure 3.5 - Problematic CPE-T graph
41
4
Chapter 4: Results and Discussion
In the following Figures the blue circles connected with solid lines show how
CPE2-T (the bulk capacitance of the suspension) changes over for each of the
bacterial-antibiotic pairs tested. The error bars are placed on each CPE2-T value
represent the estimate of the fitting-error provided by the software (typically, around
1.5% of the value). The squares show “true” concentration (CFU/ml) of viable bacteria in
the system at those points in time, as estimated using plate counts of aliquots drawn at
those points in time.
Figure 4.1 - Escherichia coli + Ampicillin Results
Control - CPE-T vs Time
3.20E-12
1.00E+06
CPE2-T
CFU/mL
3.00E-12
CFU/mL
CPE-T
1.00E+05
2.80E-12
1.00E+04
2.60E-12
2.40E-12
1.00E+03
0
1
2
Time (hrs)
3
Figure 4.1a – E. coli with no antibiotic
42
4
0.5mg/L - CPE-T vs Time
1.20E-11
1.E+07
CFU/mL
1.E+06
1.05E-11
1.E+05
9.75E-12
1.E+04
9.00E-12
CFU/mL
CPE-T
CPE2-T
1.13E-11
1.E+03
0
1
Time2(hrs)
3
4
Figure 4.1b – E. coli with 0.5mg/L Ampicillin
1mg/L - CPE-T vs Time
1.15E-11
1.E+07
CFU/mL
1.E+06
1.05E-11
1.E+05
1.00E-11
1.E+04
9.50E-12
CFU/mL
CPE-T
CPE2-T
1.10E-11
1.E+03
0
1
2
Time (hrs)
3
4
Figure 4.1c – E. coli with 1mg/L Ampicillin
2mg/L - CPE-T vs Time
3.10E-12
1.E+05
CPE2-T
CFU/mL
CPE-T
1.E+04
2.85E-12
1.E+03
2.73E-12
2.60E-12
1.E+02
0
1
2
Time (hrs)
3
Figure 4.1d – E. coli with 2mg/L Ampicillin
43
4
CFU/mL
2.98E-12
4mg/L - CPE-T vs Time
9.60E-12
1.E+05
CPE2-T
CFU/mL
8.80E-12
1.E+04
CFU/mL
CPE-T
9.20E-12
8.40E-12
8.00E-12
1.E+03
0
1
2
3
Time (hrs)
4
Figure 4.1e – E. coli with 4mg/L Ampicillin
8mg/L - CPE-T vs Time
1.16E-11
1.E+04
CPE2-T
CFU/mL
1.08E-11
1.E+03
CFU/mL
CPE-T
1.12E-11
1.04E-11
1.00E-11
1.E+02
0
1
Time2(hrs)
3
4
Figure 4.1f – E. coli with 8mg/L Ampicillin
16mg/L - CPE-T vs Time
7.50E-12
1.E+04
CPE2-T
CFU/mL
6.90E-12
1.E+03
6.60E-12
6.30E-12
1.E+02
0
1
2
Time (hrs)
3
Figure 4.1g – E. coli with 16mg/L Ampicillin
44
4
CFU/mL
CPE-T
7.20E-12
32mg/L - CPE-T vs Time
7.50E-12
1.E+04
CPE2-T
CFU/mL
7.00E-12
1.E+03
CFU/mL
CPE-T
7.25E-12
6.75E-12
6.50E-12
1.E+02
0
1
Time2(hrs)
3
4
Figure 4.1h – E. coli with 32mg/L Ampicillin
64mg/L - CPE-T vs Time
8.50E-12
4.E+03
CFU/mL
3.E+03
8.00E-12
2.E+03
7.75E-12
1.E+03
7.50E-12
CFU/mL
CPE-T
CPE2-T
8.25E-12
0.E+00
0
1
Time2(hrs)
3
4
Figure 4.1i – E. coli with 64mg/L Ampicillin
128mg/L - CPE-T vs Time
6.65E-12
1.E+03
CPE-T
CFU/mL
1.E+03
CPE-T
8.E+02
6.5E-12
6.E+02
4.E+02
6.425E-12
2.E+02
6.35E-12
0.E+00
0
1
2
Hours
3
Figure 4.1j – E. coli with 128mg/L Ampicillin
45
4
CFU/mL
6.575E-12
Figure 4.2 - Escherichia coli + Chloramphenicol Results
Control- CPE-T vs Time
8.00E-12
1.00E+07
CFU/mL
1.00E+06
7.60E-12
1.00E+05
7.40E-12
1.00E+04
7.20E-12
CFU/mL
CPE-T
CPE-T
7.80E-12
1.00E+03
0
1
2
Time (hrs)
3
4
Figure 4.2a – E. coli with No Chloramphenicol
.5mg/L - CPE-T vs Time
4.10E-12
1.00E+06
CPE-T
CFU/mL
CPE-T
1.00E+05
3.30E-12
1.00E+04
2.90E-12
2.50E-12
1.00E+03
0
1
2
3
Time (hrs)
Figure 4.2b – E. coli with 0.5mg/L Chloramphenicol
46
4
CFU/mL
3.70E-12
1mg/L - CPE-T vs Time
2.30E-12
1.00E+07
CFU/mL
1.00E+06
2.10E-12
1.00E+05
2.00E-12
1.00E+04
1.90E-12
CFU/mL
CPE-T
CPE-T
2.20E-12
1.00E+03
0
1
2
3
Time (hrs)
4
Figure 4.2c – E. coli with 1mg/L Chloramphenicol
2mg/L - CPE-T vs Time
8.20E-12
1.00E+05
CPE-T
CFU/mL
8.00E-12
CFU/mL
CPE-T
1.00E+04
7.80E-12
1.00E+03
7.60E-12
7.40E-12
1.00E+02
0
1
2
3
Time (hrs)
4
Figure 4.2d – E. coli with 2mg/L Chloramphenicol
4mg/L - CPE-T vs Time
1.15E-11
1.00E+05
CPE-T
CFU/mL
1.10E-11
CFU/mL
CPE-T
1.00E+04
1.05E-11
1.00E+03
1.00E-11
9.50E-12
1.00E+02
0
1
2
Time (hrs)
3
Figure 4.2e – E. coli with 4mg/L Chloramphenicol
47
4
8mg/L - CPE-T vs Time
2.16E-12
1.00E+05
CPE-T
CFU/mL
CPE-T
1.00E+04
2.04E-12
1.00E+03
CFU/mL
2.10E-12
1.98E-12
1.92E-12
1.00E+02
0
1
Time2(hrs)
3
4
Figure 4.2f – E. coli with 8mg/L Chloramphenicol
16mg/L - CPE-T vs Time
8.10E-12
1.00E+05
CPE-T
CFU/mL
7.90E-12
CFU/mL
CPE-T
1.00E+04
7.70E-12
1.00E+03
7.50E-12
7.30E-12
1.00E+02
0
1
2
Time (hrs)
3
4
5
Figure 4.2g – E. coli with 16mg/L Chloramphenicol
32mg/L - CPE-T vs Time
7.7E-12
1.00E+05
CPE-T
CFU/mL
7.5E-12
CFU/mL
CPE-T
1.00E+04
7.3E-12
1.00E+03
7.1E-12
6.9E-12
1.00E+02
0
1
2
Time (hrs)
3
4
Figure 4.2h – E. coli with 32mg/L Chloramphenicol
48
64mg/L - CPE-T vs Time
7.90E-12
1.00E+04
CPE-T
CFU/mL
7.50E-12
1.00E+03
CFU/mL
CPE-T
7.70E-12
7.30E-12
7.10E-12
1.00E+02
0
1
2
3
Time (hrs)
4
Figure 4.2i – E. coli with 64mg/L Chloramphenicol
128mg/L - CPE-T vs Time
7.90E-12
1.00E+04
CPE-T
CFU/mL
7.40E-12
1.00E+03
7.15E-12
6.90E-12
1.00E+02
0
1
2
3
4
Time (hrs)
Figure 4.2j – E. coli with 128mg/L Chloramphenicol
49
CFU/mL
CPE-T
7.65E-12
Figure 4.3 - Pseudomonas aeruginosa + Gentamicin Results
Control- CPE-T vs Time
8.70E-12
5.00E+04
4.00E+04
3.00E+04
8.10E-12
2.00E+04
7.80E-12
CPE-T
1.00E+04
CFU/mL
7.50E-12
0.00E+00
0
1
2 Time (hrs) 3
4
5
Figure 4.3a – P. aeruginosa with 0mg/L Gentamicin
.5mg/L - CPE-T vs Time
7.8E-12
8.00E+03
CFU/mL
6.00E+03
7.4E-12
4.00E+03
7.2E-12
2.00E+03
7E-12
0.00E+00
0
1
Time2(hrs)
3
4
Figure 4.3b – P. aeruginosa with 0.5mg/L Gentamicin
50
CFU/mL
CPE-T
CPE-T
7.6E-12
CFU/mL
CPE-T
8.40E-12
1mg/L - CPE-T vs Time
7.98E-12
8.00E+03
CFU/mL
6.00E+03
7.43E-12
4.00E+03
7.15E-12
2.00E+03
6.88E-12
CFU/mL
CPE-T
CPE-T
7.70E-12
0.00E+00
0
1
Time2(hrs)
3
4
Figure 4.3c – P. aeruginosa with 1mg/L Gentamicin
2mg/L - CPE-T vs Time
8.40E-12
2.00E+03
CFU/mL
1.50E+03
7.80E-12
1.00E+03
7.50E-12
5.00E+02
7.20E-12
CFU/mL
CPE-T
CPE-T
8.10E-12
0.00E+00
0
1
2
3
Time (hrs)
4
Figure 4.3d – P. aeruginosa with 2mg/L Gentamicin
4mg/L - CPE-T vs Time
1.2E-11
5.00E+03
CFU/mL
4.00E+03
CPE-T
3.00E+03
1E-11
2.00E+03
9E-12
1.00E+03
8E-12
0.00E+00
0
1
2
Time (hrs)
3
4
Figure 4.3e – P. aeruginosa with 4mg/L Gentamicin
51
CFU/mL
CPE-T
1.1E-11
8mg/L - CPE-T vs Time
2.10E-11
4.00E+03
CPE-T
3.50E+03
CFU/mL
3.00E+03
2.50E+03
1.50E-11
2.00E+03
1.50E+03
1.20E-11
CFU/mL
CPE-T
1.80E-11
1.00E+03
5.00E+02
9.00E-12
0.00E+00
0
1
2
Time (hrs)
3
4
5
Figure 4.3f – P. aeruginosa with 8mg/L Gentamicin
16mg/L - CPE-T vs Time
2.20E-11
3.50E+03
CPE-T
3.00E+03
CFU/mL
2.50E+03
2.00E+03
1.60E-11
1.50E+03
CFU/mL
CPE-T
1.90E-11
1.00E+03
1.30E-11
5.00E+02
1.00E-11
0.00E+00
0
1
2 Time (hrs) 3
4
5
Figure 4.3g – P. aeruginosa with 16mg/L Gentamicin
32mg/L - CPE-T vs Time
1.60E-11
2.E+03
CFU/mL
2.E+03
1.30E-11
1.E+03
1.15E-11
5.E+02
1.00E-11
0.E+00
0
1
2 Time (hrs) 3
4
5
Figure 4.3h – P. aeruginosa with 32mg/L Gentamicin
52
CFU/mL
CPE-T
CPE-T
1.45E-11
64mg/L - CPE-T vs Time
1.00E-11
3.00E+03
CPE-T
CFU/mL
2.50E+03
9.75E-12
9.50E-12
1.50E+03
1.00E+03
CFU/mL
CPE-T
2.00E+03
9.25E-12
5.00E+02
9.00E-12
0.00E+00
0
1
Time2(hrs)
3
4
Figure 4.3i – P. aeruginosa with 64mg/L Gentamicin
128mg/L - CPE-T vs Time
1.40E-11
6.00E+03
CPE-T
CFU/mL
5.00E+03
1.25E-11
1.10E-11
3.00E+03
2.00E+03
9.50E-12
1.00E+03
8.00E-12
0.00E+00
0
1
2
Time (hrs)
3
4
5
Figure 4.3j – P. aeruginosa with 128mg/L Gentamicin
53
CFU/mL
CPE-T
4.00E+03
Figure 4.4 - Pseudomonas aeruginosa + Amikacin Results
Control- CPE-T vs Time
1.50E-12
2.E+04
CPE-T
2.E+04
CFU/mL
2.E+04
1.E+04
1.20E-12
1.E+04
9.E+03
1.05E-12
7.E+03
9.00E-13
5.E+03
0
1
2
3
Time (hrs)
4
Figure 4.4a – P. aeruginosa with 0mg/L Amikacin
0.5mg/L - CPE-T vs Time
9.40E-12
4.E+04
3.E+04
3.E+04
2.E+04
8.20E-12
2.E+04
1.E+04
7.60E-12
CPE-T
6.E+03
CFU/mL
7.00E-12
1.E+03
0
1
2
Time (hrs)
3
Figure 4.4b – P. aeruginosa with 00mg/L Amikacin
54
4
CFU/mL
CPE-T
8.80E-12
CFU/mL
CPE-T
1.35E-12
1mg/L - CPE-T vs Time
1.76E-12
CPE-T
2.E+04
2.E+04
1.60E-12
CFU/mL
CPE-T
1.68E-12
3.E+04
CFU/mL
1.E+04
1.52E-12
6.E+03
1.44E-12
1.E+03
0
1
2
3
Time (hrs)
4
Figure 4.4c – P. aeruginosa with 1mg/L Amikacin
2mg/L - CPE-T vs Time
1.08E-11
3.E+04
CPE-T
CFU/mL
3.E+04
CPE-T
2.E+04
9.40E-12
2.E+04
CFU/mL
1.01E-11
1.E+04
8.70E-12
5.E+03
8.00E-12
0.E+00
0
1
2
3
Time (hrs)
4
Figure 4.4d – P. aeruginosa with 2mg/L Amikacin
4mg/L - CPE-T vs Time
1.08E-11
3.E+04
CFU/mL
2.E+04
CPE-T
1.01E-11
2.E+04
9.40E-12
1.E+04
8.70E-12
5.E+03
8.00E-12
0.E+00
0
1
2
Time (hrs)
3
4
Figure 4.4e – P. aeruginosa with 4mg/L Amikacin
55
CFU/mL
CPE-T
8mg/L - CPE-T vs Time
9.00E-12
4.E+03
CPE-T
4.E+03
CFU/mL
8.40E-12
3.E+03
7.80E-12
CFU/mL
CPE-T
3.E+03
2.E+03
2.E+03
7.20E-12
1.E+03
5.E+02
6.60E-12
0.E+00
0
1
2
3
Time (hrs)
4
Figure 4.4f – P. aeruginosa with 8mg/L Amikacin
16mg/L - CPE-T vs Time
1.60E-12
3.E+03
CPE-T
CPE-T
CPE-T
2.E+03
1.30E-12
1.E+03
1.15E-12
CFU/mL
2.E+03
1.45E-12
5.E+02
1.00E-12
0.E+00
0
1
2
3
Time (hrs)
4
Figure 4.4g – P. aeruginosa with 16mg/L Amikacin
32mg/L - CPE-T vs Time
1.50E-11
3.E+03
CPE-T
CPE-T
3.E+03
CPE-T
2.E+03
1.20E-11
2.E+03
1.E+03
1.05E-11
5.E+02
9.00E-12
0.E+00
0
1
Time2(hrs)
3
Figure 4.4f – P. aeruginosa with 32mg/L Amikacin
56
4
CFU/mL
1.35E-11
64mg/L - CPE-T vs Time
7.80E-12
4.E+03
CPE-T
CFU/mL
3.E+03
3.E+03
2.E+03
7.40E-12
2.E+03
CFU/mL
CPE-T
7.60E-12
1.E+03
7.20E-12
5.E+02
7.00E-12
0.E+00
0
1
2
Time (hrs)
3
4
5
Figure 4.4h – P. aeruginosa with 64mg/L Amikacin
128mg/L - CPE-T vs Time
8.00E-12
6.E+03
CPE-T
CFU/mL
5.E+03
7.80E-12
7.60E-12
3.E+03
CFU/mL
CPE-T
4.E+03
2.E+03
7.40E-12
1.E+03
7.20E-12
0.E+00
0
1
2
Time (hrs)
3
4
5
Figure 4.4i– P. aeruginosa with 128mg/L Amikacin
Upon visual inspection, it can be seen that for controls (no antibiotics) and for certain
low concentrations, the trend is clearly increasing. The CPE2-T values clearly rise over
time, with no overlap of the error bars between the values recorded at t=0 and t=4 hrs.
Similarly, some of the cases with the highest concentrations of bactericidal antibiotics
(Gentamicin and Amikacin) showed clear decreases – with the values at time t=4hrs
clearly lower than those at t=0. However, many data sets with intermediate
57
concentrations of antibiotics do not show such clear trends. A more rigorous analysis
was thus needed.
Since the initial CPE2-T value for each sample was different (because they
contained different numbers of viable bacteria), we normalized these data series by
plotting percent change ( [CPE2-T (t) - CPE2-T (0) ] / CPE2-T (0)) over time. This
allowed for easier comparisons between data series, and would further aid in
visualization of MIC. Such plots are shown in Figure 4.5. (For the sake of clarity, only
select concentration, typically the control and concentrations at and around the MIC, are
shown).
At any antibiotic concentration above the MIC, CPE2-T values would decrease or
remain static over time depending on if the antibiotic was bacteriostatic or bactericidal.
At antibiotic concentrations below the MIC, CPE2-T values would increase over time.
The antibiotic concentration at which CPE2-T began not to display an increase over time
was determined to be the MIC. This can be seen in Figure 4.5 (a), where 8mg/L of
Ampicillin generates a decrease in CPE2-T over time, while 4mg/L shows an increase.
58
E. coli + Ampicillin
0.15
Control
Change in Bulk Capacitance:
[ Cb(t) - Cb(0) ] / Cb(0)
0.1
0.05
4 mg/L
0
-0.05
8 mg/L
-0.1
16 mg/L
-0.15
0
1
2
3
Time (hrs)
E. coli + Chloramphenicol
0.15
Control
Change in Bulk Capacitance:
[ Cb(t) - Cb(0) ] / Cb (0)
0.1
0.05
1 mg/L
0
2mg/L
-0.05
-0.1
16 mg/L
-0.15
0
1
2
Time (hrs)
59
3
P. aeruginosa + Gentamicin
0.3
Change in Bulk Capacitance:
[ Cb(t) - Cb(0) ] / Cb (0)
0.2
Control
0.1
0.5 mg/L
0
-0.1
1 mg/L
-0.2
64 mg/L
-0.3
0
1
2
Time (hrs)
3
P. aeruginosa + Amikacin
0.3
Control
Change in Bulk Capacitance:
[ Cb(t) - Cb(0) ] / Cb (0)
0.2
0.1
1 mg/L
0
-0.1
2 mg/L
-0.2
4 mg/L
-0.3
0
1
Time (hrs)
2
3
Figure 4.5: Antibiotic Susceptibility Plots for Different Antibiotic-Bacteria Pairs
Even with this visualization, trends could be disputed in certain cases: such as in
Figure 4.5 (b), where for E. coli in 2mg/L of Chloramphenicol, one could make the case
60
is either for stasis or for death. To resolve such doubts in an objective manner, we fit all
measured bulk capacitance (CPE2-T) values in each data series to Equations 3.4 using
RTM software. A typical fit performed by RTM is shown in figure 4.6.
Figure 4.6 – RTM Generated Graph of Predicted and Actual CPE-T vs Time
As seen in Figure 4.6, RTM generates values for the specific growth rate (k), and
calculates a P-value for the null hypothesis (that the value of k is zero). Table 4.1
provides a summary of the k and p values. If bacteria were proliferating, k will be >0, if
bacteria were dying k would be <0, and if bacteria remained static then, k ≈ 0.
Since k was never actually exactly zero, the P-value was used to decide whether
to accept or reject the null hypothesis that k is statistically zero. P-values ranged from 0
to 1, and if a P-value was greater than 0.9 (90% confidence) for a data set, the null
hypothesis is accepted, meaning k is (statistically) considered zero. Therefore, data sets
with a positive k value and a P-value of < 0.9 were considered to be exhibiting bacterial
61
growth. Similarly, systems for which a negative k value is obtained along with a P-value
of < 0.9 were considered to be exhibiting bacterial death. Additionally, if P > 0.9 the data
set was considered to be exhibiting bacterial stasis, regardless of the k value.
62
Antibiotic
Concentrati
on
Value of K from eqn.() calculated using Excel Linear Regression software
with 90% confidence intervals in parentheses
Escherichia coli
ATCC 25922
Pseudomonas aeruginosa
ATCC 27853
(mg/l)
Ampicillin
Chloramphenicol
Gentamicin
Amikacin
Control
2.3
(0.24)
2.39
(0.24)
2.04
(0.275)
0.08
(0.86)
0.5
3.28
(0.65)
1.52
(0.47)
-3.02
(0.57)
0.40
(0.23)
1
0.99
(.015)
0.010
(0.428)
-0.66
(0.21)
0.14
(0.79)
2
0.06
(0.84)
0.17
(0.93)
-0.01
(0.09)
-0.44
(.71)
4
0.33
(0.44)
0.99
(0.92)
-1.74
(0.12)
-0.06
(.89)
8
-0.52
(0.73)
-0.01
(0.99)
-0.31
(0.67)
-2.26
(0.51)
16
-0.51
(0.146)
0.00
(1)
-3.80
(.072)
-0.07
(.21)
32
-1.35
(0.04)
0.00
(1)
-0.06
(0.18)
-0.08
(.89)
64
-0.03
(.87)
0.00
(1)
-0.16
(0.89)
-0.11
(0.26)
128
-0.002
(0.49)
0.00
(1)
-2.47
(0.02)
-0.15
(0.04)
Table 4.1: Statistical Analysis of CPE2-T vs. time data for bacteria with loads ~103
CFU/ml using RTM
63
Conclusions In this work we were initially able to demonstrate that our electrical based method
was capable of detecting bacterial growth, death, and stasis at ~103 CFU/mL. As
mentioned earlier, the capability to measure these phenomena at such low
concentrations may be relevant in a clinical setting for several reasons. First, it may
possible to eliminate the initial overnight plating and isolations steps required to achieve
a high bacterial load and appropriate optical density. Eliminating this step would greatly
reduce the time needed to perform an AST as the preculturing process takes ~24 hours
(Jorgensen and Ferraro 2009). Additionally, plating overnight cultures and isolating
cultures require manual labor that may only be scheduled for certain times during the
day, delaying the process even further. These manual labor requirements could also be
avoided with the automation of our process as no plates would be required. Second, it
may provide a more accurate MIC as clinically relevant bacterial concentrations are low
for many infections, and MIC values change for various antibiotics outside of their
previously known ranges (Gaieski, Mikkelsen et al. 2010). Finally, this method will
provide the effect an antibiotic is having on an unknown microorganism, which is vital
information for some infections.
This method will need to be tested against many different antibioticmicroorganism pairs before it would be ready to be tested in a clinical setting. However,
once tested against a larger panel and automated, this method could prove to be a
more efficient and time saving technique for determining MIC and antibiotic
susceptibility.
64
Chapter 5: Modeling the Inoculum Effect
Mathematical modeling can provide more rigorous explanation for the differences we
observed for the behavior of antibiotics against bacterial loads of 10 3 CFU/ml vs.
against loads of 105 CFU/ml. In this chapter, we outline our preliminary attempts at
developing such a model.
Outline of Mathematical Model: Our physical situation consists of bacterial cells
suspended in broth, with the interior of the bacterial cells separated from the broth by
the bacterial cell membranes. If one conceptually lumps together the volumes of all cells
in a suspension, this situation is accurately described by a classic problem in the study
of diffusion known as the “two compartment model”. Transport of species in this model
is based off of Fick’s First Law of Diffusion. This law states that particles will travel from
areas of high particle concentration to low concentration. Additionally, the magnitude of
flux will be proportional to this concentration gradient between these areas of varying
concentration. A schematic of this model can be seen in Figure 5.1.
Figure 5.1 – Diffusion across a thin membrane (SparknotesDiffusion)
65
The scope of this model can be expanded to bacteria placed in an antibiotic solution,
where bacteria can be modeled as the area of low antibiotic concentration and the
surrounding solution as the area of high antibiotic concentration. Bacteria have the
ability to react away some of the antibiotic that enter them, however. To describe this
phenomena, we follow the conservation mass, which can be seen in equation 1.
Equations 5.2 & 5.3 describe this conservation of mass by stating that the rate of
accumulation (or depletion) of antibiotic in the environment is equal to the rate at which
antibiotic is transported into the bacteria via diffusional flux through bacterial
membranes. Also, the rate of accumulation of antibiotic in the cell is equal to the rate at
which antibiotics are transported into the cells via diffusional flux through the
membranes minus a rate at which bacteria are able to react away antibiotics within
them. In these equations, Venv is the volume of the environment, Cenv is the
concentration of antibiotic in the environment, Vcell is the volume of a single bacterial
cell, Ccell is the concentration within a cell, J is flux, Amembrane is the area of a bacterial
membrane, R is the rate at which antibiotics are reacted away, and n is the number of
cells present in solution.
5.1)
5.2)
5.3)
Accum = In – Out + Generation - Consumed
𝑑
𝑑𝑡
𝑑
𝑑𝑡
(𝑉𝑐𝑒𝑙𝑙 𝐶𝑐𝑒𝑙𝑙 ) = 𝐽 ∗ 𝐴𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 − 𝑉𝑐𝑒𝑙𝑙 ∗ 𝑅
(𝑉𝑒𝑛𝑣 𝐶𝑒𝑛𝑣 ) = −𝐽 ∗ 𝐴𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒
Where flux (J) can be described by equation 5.4 based on Fick’s First Law of
Diffusion, P being the permeability of the membrane.
66
5.4)
𝐽=
𝐷∗𝐻
δ
∗ (𝐶𝑒𝑛𝑣 − 𝐶𝑐𝑒𝑙𝑙 ) = 𝑃 ∗ (𝐶𝑒𝑛𝑣 − 𝐶𝑐𝑒𝑙𝑙 )
Finally, Vcell and Venv can be divided through both sides of equations 2 and 3 as they will
remain constant throughout the model, and equation 4 can be used to replace J. These
simplifications yield Equations 5.5 and 5.6, which describes the change in antibiotic
concentration in the cell and in the environment.
5.5)
5.6)
𝑑𝐶𝑐𝑒𝑙𝑙
𝑑𝑡
𝑑𝐶𝑒𝑛𝑣
𝑑𝑡
=
=
𝐴𝑐𝑒𝑙𝑙
𝑉𝑐𝑒𝑙𝑙
𝐴𝑐𝑒𝑙𝑙
𝑉𝑒𝑛𝑣
∗ 𝑃 ∗ (𝐶𝑒𝑛𝑣 − 𝐶𝑐𝑒𝑙𝑙 ) − 𝑅
∗ 𝑁 ∗ 𝑃 ∗ (𝐶𝑒𝑛𝑣 − 𝐶𝑐𝑒𝑙𝑙 )
With appropriate numerical values chosen for various parameters such as Acell, Vcell,
N, P and R, Equations 5.5 and 5.6 can be solved simultaneously as a system of
“coupled” ordinary differential equations (ODEs) to yield information on how the
concentration of antibiotic within the cells (Ccell) and in the broth (Cenv) change with time.
It is expected that bacteria that are susceptible to an antibiotic present at a given
concentration in the broth will show accumulation of the antibiotic within the bacterial
cells, while those resistant will be able to “clear” the antibiotic from within the bacteria –
either completely or partially.
67
Choice of Parameters: Since the shape of both P. aeruginosa, and Escherichia Coli can
be considered to be ellipsoids (prolate spheroids), the volume and surface area of
individual cells were calculated using equations 5.7 and 5.8.
5.7)
5.8)
4
𝑉 = 𝜋𝑎𝑏𝑐
3
𝐴 = 4𝜋 (
𝑎1.6 𝑏1.6 +𝑎1.6 𝑐 1.6 +𝑏1.6 𝑐 1.6
3
1/1.6
)
Where a, b, and c are the three different radiuses of the prolate spheroid for a
bacterium. These radiuses and the prolate spheroid shape are depicted in Figure 5.2.
Figure 5.2 – Prolate Spheroid (TechnologyUK)
The values for a, b, c were 1 µm, 0.5 µm, 0.5 µm respectively for E. coli, and 2 µm, .75
µm, and .75 µm for P. aeruginosa (Pier, Lyczak et al. 2004, Phillips, Kondev et al.
2009).
68
The value of P was approximated based on the magnitude of the permeability for
hydrophilic compounds reported for P. aeruginosa. E. coli was also reported to have
100x higher permeability than P. aeruginosa, and P was altered in a subsequent section
to reflect this difference in permeability (Yoshimura and Nikaido 1982). In initial
simulations, P was set to 1x10-7 m/s. P was later changed to 1x10-5 m/s (100x higher
than previously) to demonstrate what type of effect a change in permeability would have
on the inoculum effect. Since data on reaction rates of antiobiotics within cells is scarce
(and difficult to interpret, given the variety of units chosen) we chose values of R that
yielded results that tied in with our observations (as will be described in a later section).
Originally, R was set to 2 mg/(L*s). The number of bacteria in solution (N) was chosen
between 105, 108, and 103, to reflect respectively the standard bacterial load used for
AST, the high loads tested by other investigators who were studying the “inoculum
effect”, and the low initial load that we tested using our impedance based approach.
Solving the system of coupled ODEs: The system of equations 5.5 and 5.6 (with the
values of parameters described above) was solved using an existing “library” ordinary
differential equation solver in MATLAB called “ode45”. Results (values of Cenv and Ccell)
are plotted over a duration of time (18000 seconds = 5 hrs) to determine how antibiotics
accumulate in the bacterial cells over time. This amount of time was chosen as it was
falls within the average range of time for determining MIC reported by Biomerieux’s
VITEK 2 device (a commonly used AST device in hospitals) (Vitek) and covers that
used for our own expreiments as well. At time t=0, the concentration of antibiotic within
69
the cell (Ccell) was considered to be zero, while the concentration in the broth was the
known concentration of added antibiotic (0.5, 1, 2,4, 8, etc.. mg/l)
Predicting MIC: The first step to testing this model was to verify that an MIC could be
observed: viz. that with initial concentrations of antibiotic in the environment at or above
a certain critical value, the model would show the concentration of antibiotic within the
cells rising over time, but with initial antibiotic concentration in the environment below
this critical value, the model would predict that the antibiotic is “cleared” from within the
bacterial cells.
With a bacterial load (n) of 1x105 CFU/ml, a membrane permeability P of 1x10-7 m/s, a
reaction rate R of 2 mg/(L*s) and cell dimensions corresponding to that of E. coli, the
following were observed:
1. As shown in Figure 5.3d and 5.3e, when the initial concentrations of antibiotic in
the environment were 8 mg/l and 16 mg/l respectively, the concentrations of
antibiotic within the cell (Ccell) rises over time, reaching a “plateau” value in a
fairly sort amount of time (typically in less than 600s i.e. 10 minutes). The plateau
value is less than that of the concentration outside the cell.
2. As shown in Figures 5.3b and 5.3c, when the initial concentrations of antibiotic in
the environment was 2mg/l and 4 mg/l respectively, the antibiotic is effectively
“cleared” from the cell. Our simulations shows the concentration turning negative
– but this is an artifact arising from the mathematics. In effect, the simulations
predict that the concentration of antibiotic within the cell goes to zero.
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3. With the control (no antibiotic in the environment), as expected – the
concentration of antibiotic within the cell remains zero.
We attribute the observed changes in the behavior of the antibiotic concentration within
the cell (Ccell) to the relative magnitudes of the rate of transport of antibiotic into the cell
and the reaction (clearance) rate of antibiotic within the cell. When the rate of transport
of antibiotic to the interior of the cell is greater than the ability of the cell to react away
(clear) the antibiotic, the concentration of antibiotic within the cell rises. But this
increased concentration of antibiotic within the cell, in turn, reduces the rate of transport
to the cell since the latter is proportional to the difference in concentration between the
environment and the cell. Ultimately, a state is reached where transport into the cell
equals the rate of clearance. However, if the concentration at which this occurs is high –
the cells will not be able to survive such a situation, and they will die. In contrast, when
the rate of reaction (clearance) within the cell exceeds the rate of transport to the cell,
the concentration of antibiotic within the cell does not rise from its initial value of zero.
Our simulation (due to our not limiting the values to positive numbers only) records this
as a decrease in the concentration to a value below zero.
Thus, for these parameters (N = 105, P = 10-7 m/s, R=2mg/(L*s) ) our simulation predict
an MIC of 8 mg/L since this is the lowest concentration of antibiotic in the suspension
(environment) for which accumulation occurs within the cell, i.e. Ccell does not remain
zero over time, but rises to a finite non-zero value. Given that the parameters chosen
were appropriate for E. coli, the fact that the MIC predicted by our simulation is within
71
the observed range of MICs for the strain we tested can be seen as a validation of our
mathematical model.
5.3a - Control – No Accumulation
72
5.3b - 2mg/L - No Accumulation
5.3c - 4mg/L - No Accumulation
73
5.3d - 8mg/L - Accumulation
5.3e - 16mg/L – Accumulation
74
F
5.3f - 128mg/L - Accumulation
Figure 5.3 – 105 CFU/mL with (a) Control (b) 2 mg/l (c) 4 mg/l (d) 8 mg/l (e) 16
mg/l (f) 128 mg/l antibiotic
Changing Bacterial Numbers: All of these same parameters were then tested when
n=103, and n=108. The results for n=103 yielded the same trends in cellular antibiotic
concentration over time as n=105.
75
5.4a - 2mg/L - No Accumulation
5.4b - 4mg/L - No Accumulation
76
5.4c - 8mg/L - Accumulation
5.4d - 16mg/L – Accumulation
77
5.4e - 128mg/L – No Accumulation
Figure 5.4 – 103 CFU/mL with (a) 2 mg/l (b) 4 mg/l (c) 8 mg/l (d) 16 mg/l (e) 128mg/L
antibiotic
These simulations show the same MICs for bacterial loads of 10 3 and 105
CFU/ml, which is consistent with our observations for E.coli. However, when n=10 8 was
tested a new trend emerged – as can be seen in Figures 5.3.
78
5.5a - 4mg/L – Ccell Falls to Zero
5.5b - 8mg/L – Ccell Falls to Zero
79
5.5c - 16mg/L – Accumulation
5.5d - 32mg/L - Accumulation
80
5.5 e - 128mg/L - Accumulation
Figure 5.5 – 108 CFU/mL with (a) 2 mg/l (b) 4 mg/l (c) 8 mg/l (d) 16 mg/l (e) 128mg/L
antibiotic
For bacterial loads of 103 and 105 CFU/ml, the volume of the cells (Vcell) was
negligible compared to the volume of fluid outside the cells (Venv). Hence, the transport
of antibiotic to the cells and their consumption within the cells did not measurably
change the concentration of antibiotic in the environment (Cenv). This is no longer the
case with bacterial loads of 108 CFU/ml. As a consequence, for all non-zero values of
Cenv, we note an observable reduction in its value over the duration of the simulation (5
hrs). Also, owing to Cenv itself decreasing over time, the concentration of antibiotic within
the bacterial cells (Ccell) also decreases in concert with Cenv after the initial rise (taking <
10 minutes) to a value proportional to the initial Cenv. Further, it is observed that the
effective MIC (taken to be the lowest concentration for which the value of Ccell does not
fall back to zero within the observed time frame of 5 hrs) is changed from 8mg/l to 16
81
mg/l. Again, this is consistent with reports in literature stating that ampicillin typically
displays a modest to minimal inoculum effect against E. coli (Hayward 1986).
Changing other parameters to capture the inoculum effect: Experiments performed by
others indicate that while certain antibiotics display minimal to modest inoculum effects
upon changing the bacterial loads from 105 to 108 CFU/ml wherein the MIC increases by
a factor of 2 to 4, others exhibit a more pronounced inoculum effect where the MIC
changes by factors as large as 128 (Eng, Smith et al. 1984). Mathematical models to
explain these observed differences are not readily available, and those that are invoke
parameters like “sensitivity of the realized MIC to the density of the bacteria expose”
(Levin and Udekwu 2010) that appear to be based on circular reasoning. However, one
of the implications of our mathematical model is that it certain combinations of reaction
rates (R) and permeabilities (P) lead to minimal inoculum effects, whereas other
combinations lead to pronounced inoculum effects.
The former is seen for the values of R and P chosen for the simulations of
Ampicillin acting upon E. coli. To get a feel for the combinations of R and P that lead to
the latter, we first start by changing the value of P from 10-7 m/s to 10-5 m/s (a hundredfold increase) and the value of R from 2 mg/(L*s) to 22 mg/(L*s). With these values of R
and P, we simulate the variation of Ccell and Cenv with bacterial loads of 108, 105 and 103
CFU/ml and display the results in Figures 5.6, 5.7 and 5.8, respectively.
82
5.6a - 128 mg/L - Accumulation
5.6b - 64 mg/L – Ccell Falls to Zero
83
5.6c - 32 mg/L – Ccell Falls to Zero
Figure 5.6 – 108 CFU/mL with (a) 128 mg/L (b) 64 mg/L (c) 32 mg/L antibiotic
5.7a - 1mg/L - Accumulation
84
5.7b - 0.5 mg/L – No Accumulation
Figure 5.7 – 105 CFU/mL with (a) 1 mg/L (b) 0.5 mg/L antibiotic
Figure 5.8 – 103 CFU/mL with 0.5mg/L antibiotic – Accumulation Occurs
85
As can be see nin Figures 5.6, the value of Ccell reaches zero within 5 hours for an initial
concentration of antibiotic in the broth (Cenv at t=0) of 64 mg/l, but accumulates within
the cells when Cenv at t=0 is 128 mg/l. On the other hand, for bacterial loads of 105
CFU/ml, the Ccell reaches zero for initial values of Cenv of 0.5 mg/l, but not when the
initial value of Cenv is 1 mg/l or higher. Finally, for bacterial loads of 103 CFU/ml, the
value of Ccell falls to zero even when the initial Cenv is 0.5 mg/l. Thus the apparent MICs
for bacterial loads of 108, 105 and 103 CFU/ml are 128, 1 and 0.5 mg/l, respectively.
It may be noted that with P. aeruginosa 28753 and gentamicin, we had observed an
apparent MIC of 0.5 mg/l when bacterial loads were ~103 CFU/ml, while previous
studies in our lab conducted using our electrical method and bacterial loads of 10 5
CFU/ml had recorded an MIC of 1 mg/l (Puttaswamy, Lee et al. 2012), and the
reference MIC value for this strain (for bacterial loads of 105 CFU/ml) is 1 to 4 mg/l
(CLSI 2007).
Thus our simulation indicates a possible cause for our observed lower values of
MIC for low bacterial loads in some cases, but not in others (viz. a change in the relative
magnitudes of the reaction rate and permeability). The same simulation also indicates
that the relative magnitudes of reaction rate and permeability could determine whether
the inoculum effect observed between loads of 105 and 108 CFU/ml is relatively modest
(changes by factors of 4 or less) or more pronounced.
86
Chapter 6: Future Work
In this piece of work we (a) demonstrated that our electrical method could be
used to perform Antibiotic Susceptibility Testing (determine apparent MICs) when
bacterial loads in the suspension tested were ~ 103 CFU/ml, something not possible
with existing technology (b) developed a mathematical model that seeks to explain why
the inoculum effect (changes to apparent MICs in concert with the bacterial load) is
more pronounced in certain combinations of bacterial strains and antibiotics – but not in
others.
In addition to determining MICs at low bacterial loads, our electrical method also
provides a direct means of observing whether the action of the antibiotic is bactericidal
or bacteriostatic at the conditions tested. This has possible relevance in helping
clinicians decide on which antibiotic to use when dealing with an infection characterized
by low bacterial loads (e.g. bloodstream infections). Further work will be needed to
demonstrate that the applicability of the method to other bacterial strains of interest –
especially clinical isolates.
Our modeling efforts are also very preliminary. This model suggests that it is the
relative values of antibiotic permeability and reaction (clearance) rate that determine the
magnitude of the “inoculum effect” in bacterial species. Although this model was able to
calculate changes in MIC that are similar to the results we observed, the permeabilities
and reaction rates of many antibiotic-bacterial pairs need to be obtained from a more
extensive literature search. Getting more accurate estimates of permeability and
reaction rates of a specific antibiotic-bacterial pairs would allow us to test our hypothesis
regarding the influence of reaction rates and permeabilites on the inoculum effect. In
87
addition, we would like to explore the option of extending our model to both explain and
account for bacteriostatic and bactericidal behavior of antibiotics. Finally, we would like
to modify either the permeability or the reaction (clearance) rate of a particular antibiotic
in a strain of interest and see if the predictions of our mathematical model are observed.
88
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