Download Recovering Information from Physiolic Time

Recovering Information from
Physiologic Time-series Data
Philip Crooke
Department of Mathematics
Data-Models-Insight
Outline
• NIV: an example of a simple model that has
complicated output.
• Stress Index: using an explicit mathematical
model to confirm a data mining observation.
• Sleep Apnea: decoding time-series data with
pattern recognition.
• A new project that combines data mining and
mathematical models.
Importance of Noninvasive
Ventilation (NIV) to Patient Care
Objective: To present a meta-analytic update on the effects of noninvasive
ventilation in the management of acute respiratory failure.
Design: Meta-analysis of randomized controlled clinical trials in acute
respiratory failure comparing NIV with standard medical therapy.
Patients: Randomized controlled trials of NIV in acute respiratory failure
were identified by search of (i) MEDLINE (1966-2000), (ii) published
abstracts from scientific meetings, and (iii) bibliographies of relevant
articles.
Measurements and Main Results: …..15 randomized controlled trials …
Conclusion: Substantial reductions in mortality and the need of
subsequent MV were associated with NIV in acute respiratory failure,
especially in the COPD subgroup. Hospital length of stay was variably
affected. Heterogeneity of treatment effects was observed.
From J.V. Peter et al., Noninvasive ventilation in acute respiratory failure—A metaanalysis update, Crit. Care Med. 30, pp. 555-562, 2002.
Ventilation using a Mask
NIV Diagram
Experimental Data with
Mechanical Lung
Patient-Ventilator Asynchrony
• Noninvasive Ventilation: Ventilation without endotracheal
intubation.
• Synchrony: Parallelism between the cycle timing and flow
demands of the patient and the responses of the mechanical
ventilator
Ventilator-Patient Interaction
• Constant Pressure Ventilation
• Ventilator applies constant pressure until the flow into the patient
is some fraction (a) of the initial flow
• Ventilator turns off and expiration starts
• Characteristics: variable inspiratory time and variable tidal
volume and end-expiratory pressure
Mathematical Model of NIV

 dVi(n )  Vi(n )
(n1)
Ri 
 Pex(n1)  Pset , t tot
 t  t i(n )
 
Ci
 dt 
 dVe(n )  Ve(n )
(n )
Re 
 Pex(n )  Ppeep , t i(n )  t  t tot
 
Ce
 dt 
n  1,2,3,

Lung Volume
Inspiratory Times for Different
Cutoff Values
Point: Simple linear model has complicated behavior.
Scatter with Cutoff Parameter
and Mask Resistance
Scatter with Expiratory
Resistance
The Stress Index (Ranieri)
Objective: To evaluate whether the shape of the airway
pressure-time curve during constant flow inflation
corresponds to evidence of tidal recruitment or tidal
hyperinflation in an experimental model of acute lung
injury.
Model:
Paw (t)  at b  c, t  0, a,b,c  
Conclusion: Tidal Recruitment when b 1 and
hyperinflation when b 1 .


Reference: P.S. Crooke, J.J. Marini and J.R. Hotchkiss, A new look at the stress index for lung injury, J.
Biol. Sci. 13(2005), 261-272.

One Compartment Model
Elastic Pressures in Lung
Airway Pressure and Flow during
Inspiration (Pig Data)
Concavity of Airway Pressure
Tidal Recruitment (b<1):
Hyperinflation (b>1):
d 2 Paw
0
dt 2
d 2 Paw
0
dt 2
Compliance Function
Pelastic 

V
C(V )
Model for Stress Index
Vi (t )
Ri Q 
 Pex  Paw (t )
C (Vi (t )  Vex )
a1  1V , 0  V  V1s

C (V )   a 2 , V12  V  V2s
 a   V, V s V
3
2
 3
Vi (t )  Qt
V1s  QT1
V2s  QT2
Stress Index via Model
 21 (a1  1Vex )Q 2
, 0  t  T1

3
 (a1  1Vex  1Qt )

2
0, T1  t  T2
d Paw 

2
dt

 2 3 (a 3   3Vex )Q 2
 (a   V   Qt )3 , T2  t  ti
3
3 ex
3


Conclusions from Model
negative
,


0

1
2
d Paw 
  0,  2  0
2
dt
 positive,   0
3

Model and Experimental Data
Classification of Inspiratory
Flows by Finite Automata
• Diagnosing sleep apnea with nasal prongs
• Breath-by-breath analysis for soft tissue
collapse in upper airway during sleep
• Use syntactic pattern recognition methods
• Reference: T. Aittokallio et al., Classification
of nasal inspiratory flow shapes by attributed
finite automata, Comp. Biomed. Res.
32(1999), 34-55.
Nasal Prong Pressure Signal
Baseline Pressure : - 75
Sample Frequency : 50 Hz
Noisy Signal
Segmenting Filter Signal
One breath : {x1, x 2 , , x n }
Partition : {x1,
x i1 | x i ,
x j1 |
| xm ,
xn }
One Segment : Sk  {xa , , x  }
 a, x   xa   (increasing)

Code Segment : I (Sk )  c, x   xa   (decreasing)

b, otherwise (flat)

Duration function : d(Sk )    a  1  2
Parameters : maximum duration and


Example : aabaabbaaabbbccccc
 0
Waveforms Types
2 - two humps
3 - three humps
12 - one hump/flat spot
13 - flat spot/hump
14 - flat spot/hump/flat spot
111 - one hump (no flat spot)
112 - one hump (big flat spot)
Hierarchy Scheme
Signal Processing
Automata
Deterministic finite
Q : set of states
- state automata (DFA) : A  (Q,,,q0 ,F)
 : alphabet
 : Q    Q transition function
q0 : initial state
F  Q : set if final states


Initial state : q  q0
Symbol : w
Next state : v  (q,w)
Termination : (q,w)  F
L(A)  {w   : (q0,w)  F}
L(A1)  {w   : w has one peak }
L(A2 )  {w   : w has two peaks}
L(A3 )  {w   : w has three peaks }
Parsing
Output Alphabet :   {h,t}
h : peak
t : plateau
Automation : a    t   write a /t
State : q
Attribute of state : mq  number of peaks found
Final State : mq  1,2,3, or more
Termination :  (q0 ,w)  p(final state); m p  1 for A1, m p  2 for A2 and m p  3 for A3

Automata for 1,2 or 3 Peaks
Word : w  w1w2
Peak :   ab*c 
Transition Function: A1, A2 or A3
δ[q[0], a] := {q[1], Null};
δ[q[0], b] := {q[0], Null};
δ[q[1], a] := {q[1], Null};
δ[q[1], b] := {q[2], Null};
δ[q[1], c] := {q[3], h};
δ[q[2], a] := {q[1], t};
δ[q[2], b] := {q[2], Null};
δ[q[2], c] := {q[3], h};

Automata for Classes 11,12,12 and 14
Automata for Classes 111 and 112
Train and Test
• Compare patterns of controls and
patients with partial upper airway
obstruction
• Find  and  (another parameter used
in separating classes 111 and 112) to
identify the highest percentage of
obstructive breaths (3623 total).
Automated Search Program for
Breathing Pattern Analysis
Rationale: More nuanced interpretation of breathing patterns could have diagnostic, prognostic, and interventional
benefits.
Hypothesis: The breathing patterns adopted by individuals having specific physiologic characteristics (such as cardiac
output and neurological conditions) is constrained by their regulatory systems and their impedance characteristics.
Problem: The system, although low-dimensional by many standards, is sufficiently high dimensional that patterns are
very difficult to identify or classify by human inspection of physiologic tracings. The tracings are long (hours) and
contain many breaths. Moreover, there is considerable noise and interpatient variability.
Approach: Apply automated (“machine learning”) algorithms to search existing and current databases to identify
breathing patterns associated with specific diagnostic or prognostic categories (sleep apnea, heart failure, neurological
failure, and ventilator intolerance).
Methods: An automated search algorithm has been constructed that compares symbol sequences derived from
physiologic tracings and identifies recurrent symbol motifs within these sequences. The sequences can be from the
same patient (seeking recurrent patterns within that patient), different patients (to identify patterns that are common to a
particular diagnostic or prognostic category), or a mixture of both.
Samples
1.
EKG
2.
EEG
3.
Dynamic Volume
4.
Pressure
5.
Leg Movement
6.
Snoring
7.
Blood Oxygen
8.
Etc.