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 meta-analysis update, Crit. Care Med. 30, pp. 555-562, 2002.
Ventilation using a Mask
NIV Diagram
C
Ri
Re
Rm
Qlung
Qmask
Qvent
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 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
Ri
dVi(n )
dt
Vi(n )
Ci
Pex(n 1) Pset, ttot
(n 1) t ti(n )
Re
dVe(n )
dt
Ve
(n )
Ce
Pex(n ) Ppeep, ti
(n ) t ttot(n )
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:
Conclusion: Tidal Recruitment when and hyperinflation when .
Paw(t)at b c, t 0, a,b,c
b 1
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
0.1 0.2 0.3 0.4 0.5 0.6V
2
4
6
Pelastic
Airway Pressure and Flow during Inspiration (Pig Data)
Concavity of Airway Pressure
Tidal Recruitment (b<1):
Hyperinflation (b>1):
02
2
dt
Pd aw
02
2
dt
Pd aw
Compliance Function
Pelastic V
C(V )
Model for Stress Index
)())((
)(tPP
VtVC
tVQR awex
exi
ii
VVV
VVV
VVV
VCs
s
s
233
22
12
111
,
,
0,
)(
22
11
)(
QTV
QTV
QttV
s
s
i
Stress Index via Model
iex
ex
ex
ex
aw
ttTQtV
QV
TtT
TtQtV
QV
dt
Pd
23333
2333
21
13111
2111
2
2
,)(
)(2
,0
0,)(
)(2
Conclusions from Model
0,
0,0
0,
3
2
1
2
2
positive
negative
dt
Pd aw
Model and Experimental Data
0.2 0.4 0.6 0.8 1 1.2t
5
10
15
20
25
Paw
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,x2,,xn}
Partition : {x1, x i 1 | x i, x j 1 | | xm , xn}
One Segment : Sk {x ,,x}
Code Segment : I Sk a, x x (increasing)
c, x x (decreasing)
b, otherwise (flat)
Duration function: d(Sk ) 12
Parameters : maximum duration and 0
Example : aabaabbaaabbbccccc
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 - state automata (DFA) : A(Q,,,q0,F)
Q : set of states
: alphabet
:Q Q transition function
q0 : initial state
F Q : set if final states
Initial state : qq0
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); mp 1 for A1, mp 2 for A2 and mp 3 for A3
Automata for 1,2 or 3 Peaks
Word : w w1w2
Peak : ab*c
Transition Function: 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};
δ[q[3], a] := {q[1], Null};
δ[q[3], b] := {q[4], t};
δ[q[3], c] := {q[3], Null};
δ[q[4], a] := {q[1], Null};
δ[q[4], b] := {q[4], Null};
δ[q[4], c] := {q[3], Null};
A1,A2 or A3
A1,A2 or A3
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.
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