Convexity, Jensens Inequality and Benefits of Noisy Mechanical Ventilation

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Improving Life Support Devices with Fractal
Inputs Management of Acute Lung Injury from Da
Nang to Today

• W.A.C. Mutch, M.D. FRCP(C)
• Professor and Vice-Chairman
• Department of Anesthesiology
• University of Manitoba
• VP Research
• Biovar Life Support Inc.

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Conduct of this Talk

• Introduction to Da Nang Lung or Acute Respiratory
  Distress Syndrome (ARDS)
• Biologically Variable Life Support
• Mechanical Ventilation
• Organ Networking Respiratory Sinus Arrhythmia
• Organ Perfusion Cardiopulmonary Bypass and
  Support for Transplantation

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Patient with Da Nang Lung
Normal
ARDS
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Definitions of Acute Lung Injury

• Acute Onset
• Bilateral Infiltrates on Chest X-ray
• PCWP lt 18 cm H2O
• PaO2 FIO2 lt 300, then ALI
• PaO2 FIO2 lt 200, then ARDS

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Improving Management of ARDS

• Better fluid management
• Better support of other end organ failure
• Understanding that mechanical ventilation can be
  injurious
• ARDSNet study low tidal volume strategies
• Understanding that variability is important to
  improve life support?

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Introduction to Biological Noise

• Noise in Breathing

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Human InstantaneousRespiratory Rate
Funk et al. Resp Res 2004
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BVV vs CMV
McMullen et al. Anesthesiology 2006
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Introduction to Mathematical Modelling of the P-V
Curve

• The Venegas Equation

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The P-V Curve in ARDS
Bigatello et al. Anesthesiology 1999
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P-V Curve Modellingwith the Venegas Equation
Venegas et al JAP 1998
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Where to Ventilate for ARDS?

• Patients with ARDS have a sigmoidal P-V curve
• Current management of ARDS says to ventilate at
  6-8 ml/kg (ARDSNet algorithm)
• In these circumstances ventilation is occurring
  on the convex portion of the Venegas curve
• Can we optimize ventilation on this convex
  portion of the P-V curve?

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Introduction to Jensens Inequality

• As Applied to the P-V Curve

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Jensens InequalityMathematical Notation
If F(P) V is any convex function defined on an
interval (r, s), and if pressure (P ) is a random
variable taking values in (r, s), then the mean
or expected value (E) at F(P) E(F(P)) gt F at the
mean or expected value of P F(E(P)). Such
conditions are met with BVV since noisy
ventilation provides a series of individualized
observations of pressure (P), that are
transformed to volume F(P) as determined by
Venegas curve fitting.
JL Jensen Acta Math 1906
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The Happy Marriage of Venegas and Jensen
Brewster et al. J R Soc Interface 2005
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Applications of the Concept

• Computational Medicine in Action

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BVV and Improved Oxygenation
Funk et al. Resp Res 2004
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The Inverse Function for theVenegas Equation
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BVV vs CMV with Recruitment
Funk et al. Resp Res 2004
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BVV and RSA
Mutch et al. Resp Res 2005
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BVV vs CMV with ARDS
Mutch et al. Resp Res 2005
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Other Applications of Biologically Variable Life
Support

• Many physiologic processes present with convex
  functions describing their behaviour
• Critical opening pressure of vascular beds is one
  such example
• Is it possible that a noisy signal as in
  biological variability is fundamental for these
  processes to be maximized?
• Jensens Inequality can explain the enhanced
  function or output with the addition of noise

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Biologically VariableDelivery of Cardioplegia
Graham et al. JTCVS 2001
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Convex Nature of Cardioplegia Flow
Aldea et al. JTCVS 99 1990
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Diastolic Dysfunction post Bypass
Graham et al. JTCVS 2001
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Cooling and Rewarmingfrom DHCA
Singal et al. 2005
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Enzymuria with DHCABVP vs Apulsatile Bypass
Singal et al. 2005
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Urine Proteomics DHCA Apulsatile CPB vs BVP
BL
Pre Arrest
1 hr Post
2 hr Post
3 hr Post
Apulsatile CPB
BVP
Nickerson et al. 2005
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Conclusions

• Injecting complexity or biological noise may well
  be important to maximize performance of life
  support devices and permit or maintain organ
  networking
• Computational biology has an important place to
  play in 21st century medicine
• Important knowledge translation can occur with
  medicine embracing computational approaches
• Jensens Inequality was first described nearly
  100 years ago. Here is we think the first
  application to medicine

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Acknowledgements
BVV Ruth Graham, Linda Girling, Craig Haberman,
Duane Funk, Leanne Docking, Stephen Kowalski,
Greg Doak, Bruce McManus, Keith Walley,
Elizabeth Walker, Gerry Lefevre BVP Ruth
Graham, Linda Girling, Keith Warrian, Darren
Thiessen, Rohit Singal, Leanne Docking, Peter
Nickerson, Gerry Lefevre BVC Ruth Graham, Linda
Girling, Keith Warrian Mathematical Modelling
John Brewster, Ian Sturdy Funding Support CIHR,
Biovar Life Support, IRAP, Respironics
Inc., Crocus Fund
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Where to and where not to Ventilate with BVV
.
c
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BVC with Capillary Closure
Graham et al. JTCVS 2001
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Relationship between Oxygenation and Compliance
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P-V Curve Fit forARDS Experimental Data
F (p)
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A Simple Convex Curvey x2 or f(x) x2
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BVV vs CMV for OLV