Professor Chris Williams from the University of Edinburgh will discuss research aimed at improving ICU patient care using condition monitoring. This is often impeded by the presence of artifacts in the data; maintaining blood pressure in critically ill patients is a key management goal and yet it is the physiological variable most prone to error. Using data from vital signs data collected from the Neuro ICU at the Southern General Hospital, Glasgow, Chris will describe work on using the the Factorial Switching Linear Dynamical System (FSLDS) and the Discriminative Switching Linear Dynamical System (DSLDS) for the detection, removal and cleaning of artifacts. Chris will also present a non-linear dynamical system for modelling the effect of drug infusions on the vital signs of patients admitted in Intensive Care Units (ICUs). More specifically the work is interested in modelling the effect of a widely used anaesthetic drug called Propofolon a patient's monitored depth of anaesthesia and haemodynamics. The approach is compared with one from the Pharmacokinetics/Pharmacodynamics (PK/PD) literature. Joint work with: Konstantinos Georgatzis, Chris Hawthorne, Partha Lal, Martin Shaw, Ian Piper. Meetup was here: https://www.meetup.com/London-Bayesian-network-Meetup-Group/events/242965982/

1. Healthcare condition monitoring using ICU
data
Chris Williams
joint work with Yvonne Freer, Konstantinos Georgatzis, Chris
Hawthorne, Partha Lal, Neil McIntosh, Ian Piper, John Quinn,
Martin Shaw, Ioan Stanculescu
School of Informatics, University of Edinburgh,
and Alan Turing Institute, London
November 2017
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2. My main research interests:
Time series understanding
Computer vision, especially object recognition, shape and
texture modelling
Semi-automation of data cleaning and preparation
Unsupervised learning
Gaussian processes
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3. Time Series Understanding
Explain the multivariate time series in terms of an
underlying set of discrete factors
Make inferences for underlying variables when
observations are corrupted by artifact
We will address such problems with various switching
linear dynamical systems (SLDS) models
BS
Time (s)
BR
0 200 400 600 800
0
100
200
HR(bpm)
20
40
60
80
Sys.BP(mmHg)
20
40
60
Dia.BP(mmHg)
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4. ICU Condition Monitoring
Population: patients receiving intensive care
Data: physiological vital signs recordings
Problems: artifact corruption, false alarms, amount of data
Goal: Determine the state of health of the patient,
uncorrupted vital signs
Image source: Wikipedia Intensive Care Unit page
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5. Overview
Factorial Switching Linear Dynamical System
Inference and Learning
FSLDS and DSLDS
Novel Regimes
Data
Results
Summary
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6. Factors Affecting Measurements
The physiological observations are affected by different
factors.
Factors can be artifactual or physiological.
30
40
50
60
Sys.BP(mmHg)
0 200 400 600 800 1000
0
20
40
60
Dia.BP(mmHg)
Time (s)
0 20 40 60 80 100
40
60
80
100
120
140
160
180
HR(bpm) Time (s)
Arterial blood sample Bradycardia
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7. Factorial Switching Linear Dynamical System
Artifactual state
Physiological state
Observations
Physiological factors
Artifactual factors
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8. FSLDS notation
st is the switch variable, which indexes factor settings, e.g.
‘blood sample occurring and first stage of TCP
recalibration’.
xt is the hidden continuous state at time t. This contains
information on the true physiology of the baby, and on the
levels of artifactual processes.
y1:t are the observations.
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9. Kalman filtering
Continuous hidden state affects some observations:
xt ∼ N(Axt−1, Q)
yt ∼ N(Cxt , R)
Kalman filter equations can be used to work compute
p(x1:t |y1:t )
Done iteratively by predicting and updating
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10. Switching dynamics
The switch variable st selects the dynamics for a particular
combination of factor settings:
xt ∼ N(A(st )
xt−1, Q(st )
)
yt ∼ N(C(st )
xt , R(st )
)
For each setting of st , the Kalman filter equations give a
predictive distribution for xt .
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11. Factor interactions
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12. Related work
Switching linear dynamical models have been studied by
many authors, e.g. Alspach and Sorenson (1972),
Ghahramani and Hinton (1996).
Applications include fault detection in mobile robots (de
Freitas et al., 2004), speech recognition (Droppo and
Acero, 2004), industrial monitoring (Morales-Menedez et
al., 2002).
A two-factor FSLDS was used for speech recognition by
Ma and Deng (2004). Factorised SLDS also used for
musical transcription (Cemgil et al., 2006).
There has been previous work on condition monitoring in
the ICU, though we are unaware of any previous studies
that use a FSLDS.
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13. Inference and Learning
For this application, we are interested in filtering, inferring
p(st , xt |y1:t )
Exact inference is intractable (Lerner and Parr, 2001)
We use the Gaussian sum approximation (e.g. Murphy,
1998)
Learning uses labelled data for different regimes, and
overwriting order of factors
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14. Example inference results
Can examine variance of estimates of true physiology ˆxt ,
e.g. for blood sample (left) and temperature probe
disconnection (right):
Time (s)
BS
0 50 100 150 200 250
Sys.BP(mmHg)
35
40
45
50
55
Dia.BP(mmHg)
20
30
40
50
Time (s)
TD
0 500 1000
Coretemp.(°C)
35
35.5
36
36.5
37
37.5
38
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15. Models: FSLDS, DSLDS
DSLDS (Georgatzis and Williams, UAI 2015)
st is predicted with a classifier
Inference for xt is similar to FSLDS
α-mixture combines FSLDS and DSLDS
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16. FSLDS and DSLDS: pros and cons
+ Knowledge engineering tells us how the factors interact
generatively
+ There is not very much labelled data
+ Normality varies per patient (multi-task learning)
- In the DSLDS discrete state distributions are predicted
directly, rather than inferred. Can encode knowledge with
informative features.
- Some events (esp. artifactual) might be easier to identify
with a discriminative approach. Harder to come up with a
generative model.
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17. Novel Regimes
There are many other factors influencing the data: drugs,
sepsis, neurological problems...
50
100
150
200
Heart rate
40
50
60
70
Dia. BP
0 200 400 600 800 1000 1200
0
50
100
SpO2
?
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18. Known Unknowns
Add a factor to represent abnormal dynamics
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19. Known Unknowns
Add a factor to represent abnormal dynamics
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20. X-factor for static 1-D data
For static data, we can use a model M∗ representing
‘abnormal’ data points.
y
p(y|s)
The high-variance model wins when the data is not well
explained by the original model
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21. X-factor with known factors
The X-factor can be applied to the static data in
conjunction with known factors (green):
y
p(y|s)
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22. X-factor for dynamic data
xt ∼ N(Axt−1, Q)
yt ∼ N(Cxt , R)
Can construct an ‘abnormal’ dynamic regime analogously:
Normal dynamics: {A, Q, C, R}
X-factor dynamics: {A,ξQ, C, R}, ξ > 1.
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23. Spectral view of the X-factor
f
S
y
(f)
0 1/2
Plot shows the spectrum of a hidden AR(5) process, and
accompanying X-factor
More power at every frequency
Dynamical analogue of the static 1-D case
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24. Data
27 patients from Neuro ICU in the Southern General
Hospital, Glasgow (15 TBI, 12 SAH)
Channels:
arterial blood pressure (ABP)
electrocardiogram (ECG)
pulse oximetry
intracranial pressure (ICP)
end tidal CO2 (EtCO2)
respiratory signal (Resp)
Downsampled to 1 Hz
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25. Annotation
46 event-types labelled, including blood sample, damped
trace, patient turning and suctioning
Damped trace events have a mean duration of over 8
hours per patient
Other significant events: blood sample, patient turning and
suctioning, noisy channels, preparation for or return from
transfer
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26. Processing pipeline
Extraction from
ICU database
Preprocessing FSLDS
Stability
detection
Made to work all together on ICU server
System operates at ∼ 10× realtime
Stability detection: need to estimate AR/ARMA parameters
for every patient individually for the stability regime
This is done by predicting intervals that are stable vs
non-stable, and using these to learn the stability regime
Software available at https:
//datashare.is.ed.ac.uk/handle/10283/855
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27. Results
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False positive rate
Truepositiverate
Blood sample
FSLDS
DSLDS
alpha−combination
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False positive rate
Truepositiverate
Damped
FSLDS
DSLDS
alpha−combination
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False positive rate
Truepositiverate
Suction
FSLDS
DSLDS
alpha−combination
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False positive rate
Truepositiverate
X−factor
FSLDS
DSLDS
alpha−combination
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28. AUC BS DT SC X
DSLDS 0.94 0.78 0.64 0.56
FSLDS 0.86 0.77 0.60 0.60
α-mixture 0.95(0.9) 0.79(0.9) 0.64(−∞) 0.61(1.4)
Blood sample performance is very good, and is potentially
useful for silencing false alarms
Damped trace is particularly interesting as it has significant
duration and is not an event caused by nursing
interventions; it is therefore particularly helpful to flag up
Suction events are complex and have a variable time
course. Also suction and position change events can have
similar effects on the patient. Position change was not
modelled with a factor in our experiments, thus it may not
be surprising if these two event types are confused
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29. Damped Trace Example
True X
True SC
True BS
True DT
00:13:00 00:13:45 00:14:30 00:15:15 00:16:00 00:16:45 00:17:30 00:18:15 00:19:00 00:19:44 00:20:29 00:21:14 00:21:59 00:22:44 00:23:29 00:24:14 00:24:59
0
50
100
150
200
250
ABP
(mmHg)
Patient damped_trace_demo
Dia.
Mean
Sys.
X −− DSLDS
X −− FSLDS
X −− alpha
SC −− DSLDS
SC −− FSLDS
SC −− alpha
BS −− DSLDS
BS −− FSLDS
BS −− alpha
DT −− DSLDS
DT −− FSLDS
DT −− alpha
0.2
0.4
0.6
0.8
1
Note imputed x-state
Our clinicians believe that showing imputed state and
flagging up artifact would be helpful
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30. Blood Sample Example
True X
True SC
True BS
True DT
00:09:00 00:09:41 00:10:22 00:11:04 00:11:45 00:12:26 00:13:07 00:13:48 00:14:30 00:15:11 00:15:52 00:16:33 00:17:14 00:17:55 00:18:37 00:19:18
0
50
100
150
200
250
ABP
(mmHg)
Patient blood_sample_demo
Dia.
Mean
Sys.
X −− DSLDS
X −− FSLDS
X −− alpha
SC −− DSLDS
SC −− FSLDS
SC −− alpha
BS −− DSLDS
BS −− FSLDS
BS −− alpha
DT −− DSLDS
DT −− FSLDS
DT −− alpha
0.2
0.4
0.6
0.8
1
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31. Summary
Quantification of the amount of artifact in this dataset,
importance of damped trace events
AUC scores are very high for blood samples (0.95), good
for damped trace (0.79), and poor for suction (0.64) and
X-factor (0.61) events
Successful implementation of a real-time system carrying
out FSLDS analysis on the raw data coming from the ICU
FSLDS/DSLDS models can be applied to other ICU
monitoring tasks (e.g. identifying sepsis) and more
generally
We are also developing models for the effect of
interventions (e.g. drug administration)
Funding: Chief Scientist Office (Scotland) CHZ/4/801
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32. References
Factorial Switching Linear Dynamical Systems applied to
Physiological Condition Monitoring.
John A. Quinn, Christopher K.I. Williams, Neil McIntosh. IEEE
Trans. on Pattern Analysis and Machine Intelligence 31(9) pp
1537-1551 (2009).
Discriminative Switching Linear Dynamical Systems applied to
Physiological Condition Monitoring. Konstantinos Georgatzis,
Christopher K. I. Williams, Proc UAI 2015.
Detecting Artifactual Events in Vital Signs Monitoring Data.
Partha Lal, Christopher K. I. Williams, Konstantinos Georgatzis,
Christopher Hawthorne, Paul McMonagle, Ian Piper, Martin
Shaw. Tech report, September 2015.
Available from http://homepages.inf.ed.ac.uk/ckiw/
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