Recovering Information from Physiologic Time-series Data Philip Crooke Department of Mathematics

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.