“Can this cool new glycaemia metric tell me if my critical care patients are going to live or die?

F. Thomas, M. Signal, J.G. Chase, G.M. Shaw

Can this new glycemia metric tell me if my critical care

patients are going to live or die?

INTRODUCTION

Critically ill patients often exhibit abnormal glycemia due to the severity of their illness. High blood glucose levels and high glycemic variability have both been independently associated with increased mortality in these patients. More recently, it was hypothesized that glucose complexity may also be associated with increased mortality.

Two studies have used Detrended Fluctuation Analysis (DFA) to investigate glucose complexity in continuous glucose monitoring (CGM)

data from critically ill patients (Lundelin 2010, Brunner 2012). Both studies reported

an association between glucose complexity and mortality in critically ill patients. The aim of this study was to extend the knowledge of glucose complexity in critically ill adults by investigating the effects of CGM device type/calibration and CGM sensor location on DFA results.

METHODS

Monofractal Detrended Fluctuation Analysis (DFA)

Monofractal DFA results in an exponent, H - the Hurst coefficient, which describes the scaling properties of a time series

The larger the

H

, the less ‘complex’ the signal is

Multifractal Detrended Fluctuation Analysis (MFDFA)

If scaling properties of the signal are not independent on time and space, multifractal DFA should be used to analyze the signal. For multifractal signals, H is dependent on q-order statistical moments and

the complexity of the signal is better described by the ‘Multifractal

Spectrum’

CONCLUSION

This study clearly highlights where care should be taken in future DFA studies. Monofractal DFA results were

sensitive to the type of CGM device used to collect the glucose data. Multifractal DFA results were not always

consistent with monofractal DFA results. The width of the multifractal spectrums suggests that multifractal DFA is more appropriate for this type of data. Finally, an

association between DFA results and mortality could not be detected in this limited data set.

Failing regulatory

system

Lower Glucose complexity = Higher

Hurst coefficient Mortality?

“The monofractal structure of biomedical signals are defined by a single power law exponent, and assumes that scale invariance is

independent on time and space” Ihlen 2012

X(ct) = c

X(t)

RESULTS

DFA

MFDFA

There was no clear associations between any of the CGM parameters

tested and the shape, width or location of the multifractal spectrums (Figure 3). Furthermore, on several occasions Monofractal and Multifractal DFA

gave contradictory results and indicate that future DFA results should be interpreted with care (Figure 4).

The CGM traces obtained by multiple devices in a single patient can be very similar but produce very different multifractal spectrums

Guardian iPro2 P value Number of data sets 9 8

Scaling exponent (H) 1.43 [1.37 - 1.48] 1.56 [1.46 - 1.60]

Difference in H (iPro2 - Guardian) 0.08

Abdomen Thigh P value Number of data sets 8 9

Scaling exponent (H) 1.56 [1.46 - 1.60] 1.52 [1.50 - 1.61]

Difference in H (Thigh - Abdomen) 0.64

Lived Died P value Number of data sets 17 9

Scaling exponent (H) 1.51 [1.46 - 1.57] 1.47 [1.39 - 1.59] 0.50

CGM device type (both in abdomen)

Sensor location (both iPro2)

0.10 [0.03 - 0.20]

0.04 [-0.06 - 0.11]

Outcome mortality

Analysing calibrated SG data

Patients

This study used CGM data from 10 patients admitted to the Christchurch Hospital ICU. Patients wore Medtronic Guardian and Medtronic iPro2 devices on their abdomen, and a second iPro2 device on their thigh. This configuration allowed the effects of CGM device type and sensor location to be investigated, for each participant.

Patients 10 Age (years) 51 [39 - 64] Sex (M/F) 5/5 APACHE II 24 [17 - 27] APACHE III 85 [52 - 99] SAPS II 52 [30 - 59] LOS (days) 20 [10 - 33] Outcome (L/D) 6/4 Diabetes (None/T1/T2) 10/0/0

Table 1: Cohort Demographics

1 1.5 2 2.5 3 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 h(q) D (q ) Monofractal Mulltifractal 32 64 128 256 -5 -4 -3 -2 -1 0

Scale (segment sample size)

lo

g 2

(F

q

)

Scaling function Fq (q-order RMS)

-5 -4 -3 -2 -1 0 1 2 3 4 5 1.4 1.5 1.6 1.7 1.8 1.9 2 q Hq

q-order Hurst exponent

-5 -4 -3 -2 -1 0 1 2 3 4 5 -15 -10 -5 0 5 10 q tq

q-order Mass exponent

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 0.4 0.5 0.6 0.7 0.8 0.9 1 hq Dq

Multifractal spectrum B = Guard R = SG1 G = SG2 q =-5 q =0 q =5 q =-5 q =0 q =5 data1 tq(5) =6.1728 Hq(-5) =1.9875 Hq(0) =1.7092 data1 Dq(-5) =0.59778 hq(-5) =2.0679 Dq(0) =1 hq(0) =1.6969 Dq(5) =0.52901 hq(5) =1.3404 Slope = Hq hq max - hqmin =0.72753

Figure 1: CGM signal displaying multifractal properties with a

Hurst coefficient that varies with q order statistical moments Figure 2: Multifractal spectrum of a mono and _{multifractal signal, data supplied by Ihlen 2012}

Consistently higher

H values from iPro2

data compared to

Guardian data.

No significant

difference in sensor

location or mortality

results

Table 2: Monofractal DFA cohort results

0 0.5 1 1.5 2 2.5 -0.5 0 0.5 1 h(q) D (q )

Sensor location - SG data Abdomen Thigh 0 0.5 1 1.5 2 2.5 -0.5 0 0.5 1 h(q) D (q )

CGM device type - ISIG data Guardian iPro2 0 0.5 1 1.5 2 2.5 -0.5 0 0.5 1 h(q) D (q )

Sensor location - ISIG data Abdomen Thigh 0 0.5 1 1.5 2 2.5 -0.5 0 0.5 1 h(q) D (q )

Outcome mortality - ISIG data Lived Died 0 0.5 1 1.5 2 2.5 -0.5 0 0.5 1 h(q) D (q )

CGM device type - SG data Guardian iPro2 0 0.5 1 1.5 2 2.5 -0.5 0 0.5 1 h(q) D (q )

Outcome mortality - SG data Lived

Died

Figure 3: Multifractal spectrums comparing CGM device types, sensor locations and outcome mortality 0 0.5 1 1.5 2 2.5 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 h(q) D (q )

Mulitfractal Spectrum for two data sets with H=1.38

0 0.5 1 1.5 2 2.5 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Mulitfractal Spectrum for two data sets with H=1.39

h(q) D (q ) 0 0.5 1 1.5 2 2.5 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 h(q) D (q )

Mulitfractal Spectrum for two data sets with H=1.51

0 0.5 1 1.5 2 2.5 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 h(q) D (q )

Mulitfractal Spectrum for two data sets with H=1.57 P4 iPro - Abdomen P6 iPro - Thigh P3 Guardian - Abdomen P6 Guardian - Abdomen P3 iPro - Thigh P8 iPro - Thigh P9 iPro - Thigh P1 iPro - Thigh

Figure 4: Multifractal Spectrum comparison for data sets that had the same scaling exponent from monofractal DFA

-5 0 5 0 0.5 1 1.5 2 2.5 3

Scaling exponent as a function of q order

q S c a lin g e x p o n e n t (H ) 0 0.5 1 1.5 2 2.5 -0.5 0 0.5 1 Multifractal spectrum h(q) D (q ) 0 1 2 3 4 5 6 0 5 10 15 SG data Time (days) G lu c o s e ( m m o l/ L ) Guardian - Abdomen iPro - Abdomen Guardian - Abdomen iPro - Abdomen Guardian - Abdomen iPro - Abdomen -5 0 5 0 0.5 1 1.5 2 2.5 3

Scaling exponent as a function of q order

q S c a lin g e x p o n e n t (H ) 0 0.5 1 1.5 2 2.5 -0.5 0 0.5 1 Multifractal spectrum h(q) D (q ) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 5 10 15 SG data Time (days) G lu c o s e ( m m o l/ L ) Guardian - Abdomen iPro - Abdomen iPro - Thigh Guardian - Abdomen iPro - Abdomen iPro - Thigh Guardian - Abdomen iPro - Abdomen iPro - Thigh

Figure 5: A)This example shows average agreement between SG data for two CGMs, but the multifractal spectrums for each data set overlap. B) his example shows good agreement between SG data for each of the three CGMs, but the multifractal spectrums for each data set are quite different.