Dynamics of Blood Stream Infections

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Dynamics of Blood Stream Infections

• John G. Younger, MD
• Department of Emergency Medicine
• University of Michigan

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My Collaborative Ensemble

• University of Michigan
• Emergency Medicine
• Hangyul Chung
• Megan Cartwright
• Chemical Engineering
• Mike Solomon
• Danial Hohne
• Bioengineering
• Joe Bull
• David Li
• Center for Advanced Computing
• Andrew Caird

• University of Michigan (cont.)
• Mathematics
• Trace Jackson
• Patrick Nelson
• University of Colorado
• Applied Mathematics
• David Bortz

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Bacteremia Pathologic Presence of Bacteria in
the Circulation

• Common occurrence among in- and outpatients
• 1,200 per 100,000 general population per year
• 80,000 catheter-related infections in the US each
  year
• Attributable mortality as high as 35
• An important pathogenic contributor to sepsis

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Short Term Mortality Among Older Adults with
Serious InfectionsUM- Summer/Autumn 2007
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Clinical Features of a Human Bacteremic Episode

• Relatively Acute onset (fine one minute, not well
  the next)
• Classic systemic signs and symptoms
• Fever
• Shaking chills
• Altered consciousness and confusion
• Low blood pressure
• Measured as Present/Absent
• No reliable means of quantifying number of
  bacteria per volume
• Estimates are 102 103 live bacteria per
  milliliter of blood
• Considerable error in this measurement
• Duration is difficult to comment upon
• Antibiotics are usually started within an hour or
  so of suspected onset
• Subsequent hunt for bacteria in the blood stream
  usually reveals nothing
• Resolution?
• Suppression of bacterial detection by
  antibiotics?

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Likely Dynamic Features of A Human Bacteremic
Episode

• An uncertain t0
• Unknown y0
• Bacterial growth
• Technically logistic, but bacterial numbers never
  get near the carrying capacity.
• Exponential growth considered appropriate
• Doubling time for organisms of interest 45-60
  minutes
• Bacterial death
• Effected by rapidly available host immunity
• Filtration
• Presumably occurs by repeated bacterial passage
  through very small blood vessels, ultimately
  trapped by adhesion to a vessel wall
• Seeding
• Infected tissue can introduce bacteria back into
  the bloodstream

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The Previous Dynamical State of the Art
1959 1983
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Techniques for Quantifying Bacteria in the
Bloodstream
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Quantitative Culture Our Current Standard
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• Advantages of Mouse Models
• Strong genetic and life history similarity is
  possible
• Reasonable costs
• 15 per animal
• to and y0 can be defined
• Larger than customary bacterial numbers can be
  intravenously injected, allowing better
  quantitative, rather than qualitative,
  measurement.

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• Disadvantages to using mice
• Theyre small (18 grams)
• 800 ul of blood
• In the context of y, they can only be measured
  once
• You cannot directly determine dy/dt
• Trajectories have to be pieced together based on
  the assumption that all of the mice in any given
  experimental group are traveling in generally the
  same flow

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Modeling The Dynamics of Murine Bacteremia

• Self-Imposed Requirements
• Modeled primarily at the organ level
• Experimental methods allow quantifying bacterial
  content in various organs
• Model should be based on known physical features
  and constraints of the biological system
• Organ volume, blood volume, and blood flow
• Model should not require additional degrees of
  freedom to converge to experimental data
• Strongly avoid unmeasurable terms
• Stability analysis of the model should
  distinguish survivable and nonsurvivable
  experimental conditions
• Experimental data should correlate with stability
  regions in the model
• Some features should lend themselves to further
  modeling at a smaller scale

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Modeling The Dynamics of Bacteremia

• Experimental Plan
• Inoculate mice with S. epidermidis at t 0
• Collect quantitative cultures at t 3, ,
  48 hours of blood, liver, spleen, and lung
• Render some animals acutely immunocompromised by
  administration of cyclophosphamide prior to
  infection
• Experimental Realities
• In a murine model, organ culture can only be
  performed once
• Destructive endpoints prevent measuring dx/dt for
  any individual subject
• Quantitative culture of bacteria displays
  exponential experimental error
• Immunocompromised mice will not survive 48 hours
• Truncated experimental trajectories will be
  available
• Adhering to our requirement to avoid unmeasured
  behavior, autonomous ODEs were chosen

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Bacteremia from a Pharmacokinetic Perspective
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An Experimentalists Apology
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Astronomical Measurement Error, ca 1630
Venutian Trajectory, Autumn Sky, 2007
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Tychos Data with Biological Magnitude Noise
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Tenure for someone in life sciences.
Where a right ascension and d declination
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Bacteremic Time Courses in Normal and
Cyclophosphamide-Treated Animals
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Sampling Strategy for Finding Parameter Estimates

• Bootstrap sampling of y0 and subsequent time
  points
• 1,000 replicate samples pulled
• Each sample fitted with ode15s
• Parameter estimates summarized

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Bootstrap Estimation of Model Parameters
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Routh-Hurwitz Criteria for Stability of the Origin

• det(A) calculated for all 1,000 bootstrap
  replicates
• 95 CI for stability boundary generated

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Parameter Space Separation of Normal and
Immunocompromised Mice
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A Ton of Work Later

• In a multicompartmental linear model of
  bacteremia, chemotherapy-related immunocompromise
  appears to most strongly affect partitioning of
  bacteria out of circulating blood
• Bootstrap estimates of parameters have allowed
  something akin to statistical comparisons between
  groups, and placed a confidence region around
  det(A) 0
• We have estimated exactly one trajectory per
  experimental condition

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Refinements

• Preliminary results with a nondestructive
  measurement system
• Considering the possibility of polydisperse
  bacterial aggregate size
• Modeling the act of bacterial partitioning out of
  the bloodstream
• A soft matter experimental approach

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Luciferase
FMNH2 O2 R-CHO ? FMN R-COOH H2O hn
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Very Early Compartmentalization following an
Intravenous Bacterial Injection
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Measurement Problems Using Luminescent Bacteria
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Bacteria in the Bloodstream Probably Prefer to
Travel As Multicellular Structures
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Rationale and Implications for Polydisperse
Existence in the Bloodstream

• Bacteria at many sites of entry into the
  bloodstream exist as biofilms
• Multicellular structures with complex
  extracellular binders
• E.g., Catheters, pneumonia, urinary infections,
  dental infections
• Shear forces encountered in the bloodstream may
  not be sufficiently large to shred aggregates
• The number of bacteria in the blood at a given
  time may be the wrong metric
• Distribution of bacterial aggregate sizes may be
  more important
• Partitioning becomes a very mechanical process
• Dimensional and viscoelastic coupling to
  microscopic blood vessels

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Evaluating Bacterial Aggregate Populations
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Structural Evaluation of Potentially
Physiologically Relevant Bacterial Aggregates
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Mechanical Manipulation of Aggregates using
Microfluidic Channels
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Mechanical Manipulation of Aggregates using
Microfluidic Channels
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Mechanical Compression of Multicellular
Aggregates Evidence of Strain Hardening Behavior
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Conclusions

• Bacteremia is an important medical problem
• It has some attractive features for modeling
• The presence of bacteria in the blood or some
  other compartment is an unambiguous (bad) signal
• Dynamics of bacterial clearance amenable to
  straight-forward compartmental analysis
• Moving to smaller scales of analysis is intuitive
  and leads to well-traveled fluid dynamic and soft
  matter strategies, rather than large-scale,
  highly noisy animal systems
• Future work is directed at understanding
  mechanics of bacteria in flowing blood with an
  eye towards therapy directed at modulating the
  likelihood of filtration, rather than simply
  trying to kill the bacteria outright.

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NIGMS Computational Biology Program
Center for Computational Medicine and Biology
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