Continuous Glucose Monitoring Sensor Data-Denoising

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European Journal of Scientific Research

ISSN 1450-216X Vol.66 No.2 (2011), pp. 293-302 EuroJournals Publishing, Inc. 2011

http://www.europeanjournalofscientificresearch.com

Continuous Glucose Monitoring Sensor Data: Denoising with

Hybrid of Neural Network and Extended Kalman Filter

Algorithm

S. ShanthiDepartment of Electronics and Communication Engineering, JJ College of Engineering and

Technology, Anna Uinversity of Technology, Tiruchirappalli, Tamilnadu, India

E-mail: [email protected]

D. Kumar

Dean-Research, Periyaar Maniammai University, Vallam, Tanjore, Tamilnadu, India

E-mail: [email protected]

Abstract

Diabetes Mellitus is a chronic disease that has become the third major cause of

death around the world. To prevent the adverse effects of diabetes, people use continuous

glucose monitoring (CGM) devices. But the accuracy of CGM data is affected with time

lag, random fluctuations and noise related with sensor physics and chemistry. These noiseeffects gives a setback in using the CGM data in generation of Hypo / Hyper glycemic

alerts and control signal in artificial pancreas. This paper deals with a hybrid filtering

technique (HFT) comprising of an artificial neural network trained with extended Kalman

filter algorithm to remove all types of noise in CGM signal. The method has been evaluatedwith simulated data obtained through Glucosim and validated with the performance metric

of Root Mean Square Error. And the method is also compared with moving average andKalman filter techniques.

Keywords: Continuous Glucose Monitoring, Diabetes , Extended Kalman filter, Neural

Network, Noise effects.

1. IntroductionIn a recent survey it is found that nearly 250 million people around the world are affected with

Diabetes and this number will be in a growing trend every year. This has become a major health issueto be taken care of. Diabetes Mellitus is an auto immune disease due to the inability of the pancreas in

secreting sufficient insulin. Insulin is the hormone which facilitates the uptake of glucose from the

blood in to the body cells. Shortage of insulin leads to accumulation of glucose in blood

(Hyperglycemia) resulting in complications like Diabetic retinopathy, nephropathy and cardio vasculardiseases. Excess of insulin leads to lower glucose levels (Hypo glycemia) resulting in Diabetic Coma,

Seizures etc To avoid the complications one has to maintain their blood glucose value between 70

120 mg/dL ( Euglycemia or Normo glycemia). Regular monitoring and intensive insulin therapy canhelp reduce the risks of Diabetes. This paper addresses various types of errors in the continuous

glucose monitoring (CGM) data and a solution which can be implemented in CGM devices. As


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Continuous Glucose Monitoring Sensor Data: Denoising with Hybrid of

Neural Network and Extended Kalman Filter Algorithm 294

discussed earlier, glucose is the important fuel for the humans and its level must be maintained within

safe range. For observing the Blood glucose (BG) level , Continuous Glucose Monitoring (CGM)sensors are used[1][2]. The CGM devices can be used for a period of 5 to 7 days and the data stored in

it are applied for retrospective analysis. These CGM sensors are of minimally invasive type and are

placed in the subcutaneous tissue to measure the Interstitial fluid glucose (IG) rather than BG

concentration. There is a time lag of 5 12 minutes for the glucose to traverse from blood to interstitial

fluid. [3] The existence of BG to IG kinetics has been described in the literature[4] through a 2compartmental model.

( ) ( ) ( )1

( ) /g

d IG t dt IG t BG t

= + (1)

Where g is the static gain of BG to IG system which is equal to 1 under steady state. is the

time lag which can vary between individuals. This BG to IG kinetics acts as a linear low pass filter andintroduces a distortion in phase and amplitude as shown in figure 1.

Figure 1: Representative data taken from Kovatchev et al.,

This figure shows a comparison performed in a clinical study [5] on a Type 1 Diabetic subjectwith BG references collected every 15 minutes and measured in lab by YSI( Yellow Springs ,OH,

USA) and with Free Style Navigator CGM profile. The CGM devices try to compensate this time lag

by recalibration procedures.Apart from this calibration error, another source of error is the random noise component related

to sensor physics. [6][7] Finally the CGM signal is also affected with random fluctuations at high

frequency.[8] These noises in sensor output makes the measurement unreliable. These noise

components have to be removed prior to any signal processing application. The remaining part of thepaper is organized as follows. Section II gives a review of filtering approaches for CGM signal.

Section III describes the methodology of the work done. Section IV gives the details of HFT structure

and extended Kalman filter algorithm. Section V deals with the experimental part. and the results anddiscussion. Section VI is the conclusion.

2. Review on Filtering of CGM SignalDigital filtering techniques can be used to improve the quality of the signal by reducing the random

noise components. [9]

( ) ( ) ( )= +y t g t n t (2)

Where ( )t is the actual signal, ( )n t is the noise added with and y ( )t is the received signal

from CGM sensor. A brief overview of the basic filters used in noise removal is given below.


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295 S. Shanthi and D. Kumar

Median Filter :

A median filter take the median value of a window of N past glucose values.

Y(t) = median ( Yt , Yt-1,..Yt-N+1 ) (3)

The advantage of this filter is that it discards the effect of sudden spikes in the signal.

FIR and IIR filters :

A finite impulse response filter has the form

k=a0Yk+a1Yk-1++amYk-m (4)

where Y represents the measured glucose value and k is the filtered value which depends on the pastm measurements.

An Infinite impulse response (IIR) filter has the form

k = -a1k-1 a2k-2 - - aNk-N+ b0Yk + b1Yk-1++ bmYk-m (5)

where the current filtered output is a function of N previously filtered values and m previous

measurements. Dexcom16 patented the use of IIR filters for raw signal filtering with N = 3 and m = 3.

Medtronic patents show that the raw signals being obtained at 10 second intervals. At the end of each 1

minute intervals the lowest and highest values are removed and the remaining four are averaged to

obtain the 1 minute average.[10] From the patent of Steil and Rebrin,[11] it is found that the filters can

also be applied to the derivative of the glucose data which is useful as a part of closed loop algorithm

based on the rate of change of glucose. Kuure-Kinse et al., applied a dual rate Kalman filter for

continuous glucose monitoring[12]. The optimal estimation theory of Knobbe and Buckingham[13]showed that the use of extended Kalman filter accounts for both sensor noise and calibration

errors. Fachinetti et al., used the Kalman filtering with individualized error covariances.[14]

Facchinetti et al., discussed various aspects in modeling the errors in CGM sensor data[15] and

enhanced the accuracy through extended Kalman filteing.[16]

Commonly used filters are median filter and moving average filter. The present days filtering

algorithms are not adaptive to all intensities of noise. As per the patent [17] it is found that moving

average filter is being used in Medtronic CGM systems. Since the signal to noise ratio varies with time,

sensor and user, the filtering algorithm should intelligently adapt to inter patient and intra patient

variability.

Wiener filter and Kalman filter are the choices for adaptive filtering. Wiener filter requires the

process to be stationary. Kalman filter will do better for the time varying CGM signal. For reliable realtime monitoring and control of glucose, the filtering algorithm should account for

(i) Short term errors ( or noise) due to motion artifacts.(ii) Long term errors due to performance deterioration of sensor, Bio fouling, Inflammatory

complications etc..

(iii) Uncertainty in physiological parameters.(iv) Filtering of short term errors for the linear case is simple. To account the second

criteria, we go for non linear modeling which could be achieved with Extended Kalman

filter. But to satisfy the third criteria some artificial intelligence modeling technique is

needed. An artificial neural network which does the information processing as per the

way of biological neurons would be the best choice. A feed forward neural network

with back propagation algorithm would track the physiological variations in CGMsignal.

In this paper, we propose a Hybrid Filtering Technique (HFT) which comprises a feed forward

neural network whose weights are estimated by Extended Kalman Filter (EKF) for denoising of CGM

sensor data.

3. Research MethodGlucosim is a web based Diabetes Educator that can be used for the study of Glucose Insulin

Interaction in human. This simulator has been developed by the research team of Illinois institute of


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Technology[18] based on the pharmacokinetic model of Pucket [19]. It comprises compartmental

analysis of glucose and Insulin in Heart, Brain, Liver, Pancreas, Gastro intestinal tract, Kidney,

periphery and subcutaneous tissue etcThe input parameters of Glucosim are age, weight, exercise

duration, amount and timing of food intake in calories and insulin applied in units. For the given set of

inputs the simulator will give the glucose kinetics in blood, liver, intestine and total glucose uptake.

The datasets of blood glucose time series were simulated by setting various values to input

parameters in heuristic approach. Time lag is introduced in these glucose profiles to imitate the sensorperformance.[20] The sensor signal acts as the reference data signal. The analysis of noise in CGM

signal shows that the sensor errors are highly interdependent. However, the exact distribution of CGM

noise profiles has not been reported in the literature to date. Specifically no study has reported a

histogram of CGM error of values versus gold standard measures.[21] However, an approximate model

can be created using available literature and data.. The noisy CGM time series have been generated by

adding the appropriate noise distributions with the reference signal. The HFT method is tested first

with White Gaussian noise (WGN) and then with combination of WGN and Double exponential noise

(also called as Double Laplace distribution). The Laplace distribution is a distribution of differences

between two independent variates with identical exponential distribution. The distribution is given by

f((x) / ,b) = (1/ 2b) exp (- ( |x-| / b) ) (6)

where is a location parameter and b is a scale parameter. The double Laplace Distribution noise isgenerated separately with two different pairs of standard deviation and mean. This model would help to

imitate the sudden peaks and nadirs in CGM time series.

The HFT method is assessed with Monte Carlo simulation which allows appropriate

performance statistics to be generated. The RMSE between the filtered signal and the reference signal

are calculated. Figure 2 gives the overview of the methodology of the work.

Figure 2: Overview of the work

GlucoseProfile

from

Glucosim

Sensor

Data

Noisy

CGM

WGN, Double

Laplace Noise

HFT

FilterFiltered

CGM

Figure 3 shows a representative noise free glucose profile. The noisy CGM profile with WGN

and double Laplace noise distributions are illustrated in figure 4. The noisy CGM profile is applied to

HFT. The filtering process is carried out in two phases. First is the training phase and the second is the

testing phase. The first 10% of each glucose time series is used to train the neural network, shown in

figure 5. During this training phase, weights and bias of the neural nodes are estimated by EKF

algorithm. The network is trained to meet the performance criteria of Root Mean Square Error (RMSE)

between the actual value and filtered value to be less than 10mg/dL. Updation of weights and biases,

enables the network to capture the non linearities in the CGM time series. Once the network is trained,

the HFT is ready for testing phase. The remaining 90% of the data series can be sent for filtering.


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Figure 3: Noise free CGM time series Figure 4: CGM signal with WGN and Double

Laplace Noise

0 100 200 300 400 500 600 700 8000

20

40

60

80

100

120

140

160

Time in Minutes

GlucoseValuesinmg/d

L

Noise Free CGM Signal

0 100 200 300 400 500 600 700 800

0

20

40

60

80

100

120

140

160

180

200

Time in Minutes

GlucoseValuesin

mg/dL

CGM Signal with WGN & Double Laplace Noise

Figure 5: Noisy CGM signal with Training and Testing Data Sequences

0 100 200 300 400 500 600 700 8000

20

40

60

80

100

120

140

160

180

200

Time in Minutes

GlucoseValuesinmg/dL

CGM Signal with WGN & Double Laplace Noise

Training

DataTesting Data

4. Hybrid Filtering Technique4.1. Neural Network

The architecture of HFT filter is shown in figure 6. It is a multi layer feed forward back propagation

neural network with an input, hidden and an output layer. The output and hidden units have bias. The

input layer is connected to hidden layer and hidden layer is connected to output layer through

interconnection weights. These weights are to be decided by extended Kalman filter algorithm

described below. The non linearity in the glucose time series can very well be estimated and corrected

by EKF. The EKF provides minimum variance estimates in system applications where the dynamic

process and measurement models contain non linear relationships. Since the HFT comprises of only

one hidden layer the computational complexity is less in this network.

Figure 6: HFT Neural Network.


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Training Algorithm

The training of back propagation network involves four stages, viz

1. Initialization of weights.2. Feed forward.3. Back propagation of errors.4. Updation of weights and biases.

During first stage which is the initialization of weights, some small random values are assigned.During feed forward stage each input unit (Xi) receives an input signal and transmits this signal to each

of the hidden units Z1,Z2,..Zp. Each hidden unit then calculates the activation function(B i) and

sends its signal Zi to each output unit. The output unit calculates the activation function(Bj) to form the

response of the net for the given input pattern.[22]

During the back propagation of errors, each output unit compares its computed activation Yk

with its target value tk to determine the error. Based on the error, the factor k (k = 1,2,.m) is

computed and used to distribute the error at the output unit Yk back to all units in the hidden layer.

Similarly the factor j is computed for each hidden unit Zj. For efficient operation of back

propagation network, appropriate parameters should be assigned for training.[23]

4.2. Extended Kalman Filter

The minimum variance estimate of state vector of a dynamic discrete time process is governed by a

non linear stochastic difference equation

X(k+1) = f( X(k),w(k) ) (7)With a measurement vector,

Y(k) = h( X(k),v(k) ) (8)

Where fand h are non linear vectorial functions.[24] Wkand Vkare the vectors of process and

measurement noises respectively. w(k) and v(k) are assumed to be zero mean white noise processes

with covariance matrices Qk and Rk respectively. f is the non linear function that relates the state at

previous time step k-1 to the state at time step k. h is the non linear function that relates the state

and measurement vector. Estimation of state vector X is done similar to linear case. The time updateequations are given as follows.

Estimate of state vector :

x 1 x(k / k) (k / k),+ =

f ( 0) (9)

Estimate of Covariance matrix at kth sampling time :

P(k+1/k) = AkP(k/k) AkT

+ Wk Qk WkT. (10)

The measurement update equations are :

Kk = P( k+1/k)HkT( HkP(k+1/k) Hk

T+ VkRk Vk

T)

-1(11)

,0))h1)(y(kk /k)(k(/k)(k)/k(k 1xx11x ++++=++

1 (12)

( 1/ 1) ( ) ( 1/ ,0)k k+ + = +P k k I K H P k k (13)

Where Ak and Hkare the Jacobian matrices of the partial derivatives offand h with respect toX, whereas Wk and Vkare the Jacobian matrices of partial derivatives offand h with respect to wkand

vk respectively. Kk is the Kalman gain matrix at the kth sample and I is the identity matrix with size

as that ofX.

5. ExperimentThe proposed mechanism was implemented in the working platform of MATLAB (R2010a) to denoise

the CGM data. The proposed method has been evaluated with the data from GLUCOSIM simulator.

The data has been generated based on the time of meal, CHO(Carbohydrate content) in meal, body


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weight and duration of the simulation. A sample of input parameters is given in table 1. And one of the

generated data set with their parameters considered is shown below in table 2.

Table 1: Sample of Parameters for Simulation

Break fast Snack Lunch Snack Dinner Snack

Time (hh:mm) 08:30 12:00 13:30 18:00 20:00 22:00

CHO (mg/kg body weight) 1000 100 500 500 500 200

Body Weight (kg) 75Duration of simulation (hour) 24

The continuous glucose time series data were generated in varied ranges with ages between 10

to 75 and weight between 30 to 87 kg. The calories intake and insulin dosages are chosen in such a

way to have hypo and hyper glycemic occurances. 25 data sets were obtained through the simulator.

Each in turn were simulated n=20 times with Monte Carlo method. Thus, there are 25x20 = 500 CGM

time series in total where each is different due to the addition of noise with random parameters. The

noise sequences with variance values in the span of 10 to 200 mg2/dL

2, and different scaling and

location parameters are applied to the reference glucose profiles. The time lag for the glucose to

traverse from blood to interstitial fluid is taken to be average of 6 minutes. [20]

Table 2: Sample of generated dataset through GLUCOSIM

Blood Glucose(mg/dl)

Blood Insulin(mU/ml)

Intestinal

Glucose

Absorbtion(mg/kg min)

Stomach Glucose(mg/kg)

Total Glucose

Uptake (mg/kg

min)

Liver Glucose

Production(mg/kg min)

87 15 0 0 3.0328 1.58349

86.0751 15.4191 0.00543 124.7325 3.0409 1.58155

84.4065 14.6978 0.03773 373.1423 3.0422 1.58023

82.7931 13.9248 0.10154 619.9696 3.0414 1.57925

81.2454 13.2024 0.19601 865.2089 3.0404 1.5785

79.8082 12.5420 0.31488 984.1856 3.0406 1.57792

78.5114 11.9411 0.43591 977.9089 3.0431 1.57753

77.3589 11.3950 0.55367 971.6837 3.0471 1.5773

76.3445 10.8986 0.66822 965.4982 3.053 1.57713

75.4617 10.4476 0.77965 959.3521 3.0612 1.57701

74.7045 10.0377 0.88801 953.2451 3.0775 1.57688

74.0663 9.66527 0.99338 947.1770 3.0912 1.57683

73.5409 9.3268 1.09582 941.1475 3.1035 1.5768

73.1222 9.01922 1.19539 935.1564 3.1321 1.57676

72.8038 8.73972 1.29216 929.2034 3.1484 1.57675

With the aid of the simulator generated data set, our proposed work HFT filter comprising of

neural network and extended Kalman filter has been evaluated with Monte Carlo method and validated

with Root Mean Square Error (RMSE). The process and measurement noise variance are initializedwith q= 0.1 and r = 0.1 mg

2/dL

2respectively. Inputs to the neural network are applied as vectors of size

6 x 1. The state vector is of size 6 x 6. The IG values from the sensor are given to the networks input

layer. At hidden layer neural nodes, the weighted inputs are applied with tansigmoidal function. This

function introduces a non linearity in the model. The nodes at output layer are applied with linear

activation function. The output of the network depends upon the weights Wn

i,j of the neurons that are

determined by the EKF state estimation and correction approach. n represents nth layer and the

suffices i,j denotes the traversal of input from ith node in first layer to jth node in next layer. i =

1,2.Ni and j = 1,2,.Nj.


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5.1. Results and Discussion

The noisy CGM signals are applied to the Hybrid Filtering Technique method. The resultant output is

compared with the actual noise free CGM time series. RMSE is calculated as the performance metric.

The proposed HFT mechanism has been compared with the Moving average filter with exponential

weights and the Kalman filter to quantify the capability of HFT in denoising the combined effects of

random noise and double Laplace noise. With the trials conducted with 500 simulated data sets, it isobserved that the RMSE is minimum in HFT method compared with the other two. The experiments

were conducted with different scenarios and some representative results are listed in table 3. The

results clearly prove that the HFT mechanism is able to capture and remove the combined noise effects

in a superior way than the other methods. This shows that the artificial neural network in HFT is

trained well with physiological variations of each individual and it tracks the glucose profile perfectly

neglecting the various noise effects in the CGM. The HFT filtered output signal from the noisy version

is shown in figure 7.

Figure 7: Denoised CGM signal from HFT filter

0 100 200 300 400 500 600 700 8000

20

40

60

80

100

120

140

160

180

200

Time in Minutes

GlucoseValuesinmg/dL

Output of HFT filter

Noisy CGM

HFT Output

The correlation coefficient between the HFT filtered signals and the respective reference

signals are calculated, which gives a mean of 0.935.

Table 3: Performance Comparison of HFT Filter with Moving Average Filter(MA) and Kalman Filter(K)

Data Set ID

Root Mean Square Error ( mg/dL )

White Gaussian Noise Double Laplace Noise Combined Noise

MA

FilterK Filter

HFT

Filter

MA

FilterK Filter

HFT

Filter

MA

FilterK Filter

HFT

Filter

1 5.5 4.5 2.3 6.2 4.1 3.5 14.5 12.0 2.9

2 6.3 5.3 2.5 6.1 4.5 3.9 9.5 7.5 4.1

3 5.2 4.3 3.2 5.9 4.4 4.1 8.1 6.3 3.5

4 4.9 4.5 3.6 5.3 4.9 3.8 7.7 6.1 3.9

5 5.9 5.1 4.1 6.3 5.1 4.3 6.8 5.4 4.7

6 6.2 5.7 1.3 6.8 4.5 2.1 8.3 6.7 3.8

7 7.3 6.3 1.6 7.7 3.9 2.2 6.9 5.8 3.9

8 7.8 6.2 1.8 8.1 4.7 2.0 9.1 7.5 4.2

9 4.5 6.0 2.0 6.1 6.5 2.6 9.4 7.7 3.3

10 4.3 5.8 3.5 5.5 4.8 4.3 8.8 6.5 2.6

11 5.1 4.8 3.1 5.9 5.3 4.1 10.7 8.0 2.1

12 6.2 5.9 2.5 6.6 4.7 3.4 12.0 10.3 3.1

13 7.3 6.3 2.0 7.0 5.0 2.9 12.6 10.5 2.7

14 7.8 6.5 1.7 6.6 4.4 2.1 11.5 10.2 2.6

15 8.1 7.0 1.5 5.5 3.9 2.3 10.3 5.6 2.5


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6. Concluding RemarksThe Continuous Glucose Monitoring is very much essential for prevention of Diabetic complications.

Perfect filtering of various types of noise signals in CGM data enables it to be used for further

processing like Hypo/Hyper glycemic alert generation and control input to closed loop artificial

pancreas. Conventional filtering methods are not sufficient to track the variations of physiological

signal neglecting the noise effects. Our proposed work comprising the intelligent artificial neural

network with extended Kalman filter algorithm has proved its success in denoising the CGM signal

with simulated data sets. Further research effort is needed for real time implementation.

References[1] David C. Klonoff, Continuous Glucose Monitoring- Roadmap to 21st century diabetes

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