The authors have declared that no competing interests exist.
Continuous-time glucose monitoring (CGM) effectively improves glucose control, as oppose to infrequent glucose measurements (i.e. using Lancet Meters), by providing frequent blood glucose concentration (BGC) to better associate this variation with changes in behavior. Currently, the most widely used CGM devices rely on a sensor that is inserted invasively under the skin. Because of the invasive nature and also the replacement cost of sensors, the primary users of current CGM devices are insulin dependent people (type 1 and some type 2 diabetics). Most non-insulin dependent diabetics use only lancet glucose measurements. The ultimate goal of this research is the development of CGM technology that overcomes these limitations (i.e. invasive sensors and their cost) in an effort to increase CGM applications among non-insulin dependent people. To meet this objective, this preliminary work has developed a methodology to mathematically infer BGC from measurements of non-invasive input variables which can be thought of as a “virtual” or “soft” sensor approach. In this work virtual sensors are developed and evaluated on 20 subjects using four BGC measurements per day and eight input variables representing meals, activity, stress, and clock time. Up to four weeks of data are collected for each subject. One evaluation consists of 3 days of training and up to 25 days of testing data. The second one consists of one week of training, one week of validation, and 2 weeks of testing data. The third one consists two weeks of training, one week of validation and one week of testing data. Model acceptability is determined on an individual basis based on the fitted correlation to CGM testing data. For 3 day, 1 week, and 2 weeks training studies, 35%, 55% and 65% of the subjects, respectively, met the Acceptability Criteria that we established based on the concept of usefulness.
Recent research suggests that real-time, frequent, glucose monitoring can improve blood glucose control over infrequent monitoring provided through the use of lancet glucose meters for both insulin dependent
Hence, the motivation of this work is the development of a useful, non-invasive, subject-specific (personalized), continuous monitoring system in an effort to increase CGM among non-insulin dependent people.
To achieve this goal we seek to develop a low maintenance, high frequency monitoring system with an accuracy that is high enough to be useful for non-insulin dependent people. Moreover, this preliminary work proposes an inferential (i.e., virtual) sensor approach for predicting blood glucose concentration (BGC) from noninvasive inputs. This virtual sensor updates at the same rate as conventional physical sensor CGM devices. The model is developed from lancet BGC measurements that are obtained at a rate of four measurements per day. Since each sensor is calibrated from user data, the model developed for each person is said to be “subject-specific.” While inferential modeling of BGC has been done by a number of researchers
The main physical component of this system is a BodyMedia® armband of the type shown in
The most critical challenge in this highly complex, non-linear, multiple-input, highly underdetermined modeling problem is the estimation of a large set of dynamic and static parameters from a very small set of BGC data, with a sampling frequency of only 4 values per day. To achieve accuracy under these conditions is a significant advancement over the work of Rollins et al. and a unique accomplishment. Other challenges include adequately guarding against over-fitting, the lack of initial steady state data, low quality meal information that uses a designation of small, medium and large, and frequent and arbitrary removal of the armband monitor. Through novel modifications of the Rollins et al.
The basic objective of this work is the development of a subject-specific “soft sensor” or “virtual” sensor methodology that provides “useful” information to help individuals monitor and control their glucose more effectively than with lancet glucose meters. The most critical and challenging objective in this highly underdetermined problem is that the model must be developed from a BGC sampling rate of only four samples per day. These samples will come from the lancet meter of the subject and the idea is to transform these measurements to a CGM display frequency during the period of the day that the subject is not sleeping. This virtual sensor approach is an inferential model that is developed from measured variables that are termed inputs. This virtual sensor idea has seen wide applications in process monitoring and control applications in recent years
The information for the development of a virtual senor comes from two sources -- the response data set and the input data set. Since the information content of lancet BGC is quite limited, the proposed approach strongly relies on the input data set for information on glucose behavior. More specifically, this data set consists of meal size with three levels, six (6) variables from the BodyMedia armband, and the time of day (TOD) in minutes on the 24 hour clock. The inputs that we selected for this study from the armband are those selected by Rollins et al
|
|
---|---|
1. | Meal Size Index |
2. | Transverse accel – peaks |
3. | Heat flux – average |
4. | Longitudinal accel – average |
5. | Transverse accel – MAD |
6. | GSR – average |
7. | Energy expenditure |
8. | Time of day (TOD) |
The ability to map the available input/output information to accurate sensor measurements depends on the model structure, the model building procedure, and the inferential algorithm that we are calling the “Inferential Engine.” The model structure consists of the mathematical functions and the network that tie these functions together. The model building (i.e., identification) procedure is the process of using input/output information to estimate the values of unknown parameters in the mathematical functions. The Inferential Engine is the equation used to obtain the virtual senor measurements at the desired sampling frequency. This equation represents input selection, parameter estimates, and the use of lancet glucose measurements to enhance reliability. The purpose of this section is to describe these three components of the proposed technique in detail.
The modeling structure of this application must permit accurate parameter estimation under a small number of sampling times (
The dynamic functions for
where
Using backward difference finite derivative approximations, Eq. (1) gives (Rollins et al.,
with
such that w
Note that the number of dynamic parameters associated with each input is three. This small number is a strength that we exploit to obtain parameter estimates under limited sampling, as discussed below. The CDI model for food alone is represented by the following coupled Eqs. (5) and (6):
where v1and v2 are outputs from dynamic blocks
We also use backward difference finite derivative approximation on Eqs. (5) and (6) to give
Note there are four additional parameters. (α1,α2,α3 and α4)that need to be identified.
The function
Where t is the error term and assumed to be independently normally distributedwith mean 0 and variance
As stated in Rollins et al.
Since the degree of usefulness increases with
Note that only training data are used to compute SSE under Eq. (11).
We use the CDI network with Eqs. (1)-(9) and developed a procedure that can accurately estimate the 3(
Let
Where
Note that for fitting the SLRM, only five (5) parameters (the temporary static parameters γ0 and γi, and the permanent dynamic parameters τ
In Appendix A, a proof is given to show that for the SLRM,
In Step 1, our current procedure is to manually adjust the dynamic parameters one input at a time to find the “best” set of values for each input. Our definition of “best” will be given momentarily. In Step 2, the following reduced form of Eq. (9) is applied:
where λ0 is a temporary parameter only used in Step 2. This step is the most challenging. With a given set of initial values, either some or all the parameters are estimated simultaneously using an effective nonlinear regression algorithm. This process is the most iterative and time consuming as some parameters are manually set and fixed and the rest are estimated using the optimization algorithm. This process is iteratively repeated until no more improvement can be made in
The “best” set of modeling parameters is determined for two given scenarios. The first one only uses a Training set of data. In this scenario, the goal is to maximize
Successful model identification relies on effective selection of initial conditions and starting values for model parameters and the dynamic inputs (i.e., the
After obtaining a full set of parameter estimates, the proposed model development procedure has two more refinements. The first one is elimination of any armband inputs that adversely affect the value of
The final refinement involves the use of lancet glucose to help to reduce model bias. Since these measurements are infrequent and are not measured at a constant rate, it is not possible to build a correction model based on the correlation of residuals. The correction equation that we use comes from Rollins et al.
subject to:
For the proposed method, the development of a virtual-sensor requires 4 lancet measurements per day spread as evenly as possible over the time the subject is awake in about a 14 hour period. We did not have access to data meeting this requirement. However, from a previous study, we had physical-sensor CGM data sets which were collected with Institutional Review Board (IRB) approval, and the data sets were used to develop and evaluate the methodology. Thus, these data sets played two roles. First, for each subject, they played the role of a surrogate person, i.e., the true BGC for the purpose of evaluation. Secondly, they played the role of the lancet sampled data, i.e.,, the data used to build the virtual-sensors.
Using 22 test subjects (see
|
|
|
|
|
|
---|---|---|---|---|---|
|
|
||||
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
22 |
|
|
|
|
|
Note that, the original data sets contain meal information in terms of grams of carbohydrates, fats and proteins. The amounts were calculated from self reporting logs of the type and quantities of food eaten. Hence, the errors of these quantities are likely quite high at times and it is likely that a significant number of meals were not recorded or logged at the proper times. When we converted the quantities to an index value for meal size for this study (i.e. “1” represents small meal size, “2” for medium size, and “3” for large size), we applied the same conversion equation to all of the subjects. Thus, the quality of food information that we developed our models from in this study is quite poor. Therefore, since these results are obtained under poor food information they indicate the robustness of the technique to low quality food information.
Before evaluating model acceptability, subject 21 and 22 were rejected due to poor food information. As a result, subject 21 and 22 were removed from this research from this point on.
Model acceptability will be determined on an individual subject basis given that the models are subject-specific and each individual will only be concerned about model accuracy as it pertains to model developed for them. Thus, this study is evaluated based on the number of subject-models that meet a particular Acceptability Criteria. But we state and justify this criteria momentarily, after we present the statistics they it uses.
The first one is called the averaged error (AE) and is simply the average value of the residuals:
where
The second one is called the averaged absolute error and is similar to Eq. (15) except that the absolute difference is used for the term in the summation as follows:
A scaled AAE value to adjust for spread is used called the relative AAE (RAAE). This measure of performance is determined by dividing Eq. (16) by the standard deviation of the values used to calculate AAE as follows:
RAAE is a relative AAE statistic that accounts for large spread in the glucose variation of subjects. For replicated lancet measurements, the study in Rollins et al.
The last statistic or performance measure is
As the MAC shows, a model with an
The results of this study are given in
Subject | 1 | Yt | |||||||||||
Training | Tes hug | Testing | Meeting Criteria | ||||||||||
AE | AAE 1 RAAE | rit | AE | I AAE I RAAE | rit | AE | I AAE | RAAE 1 ri I | |||||
|
0 | 11.6 | 0.48 | 0.78 | 6.1 | 35.3 | 1.32 | 0.03 | 5.9 | 39.2 | 1..38 | 0.23 | No |
2 | 0 | 10.9 | 0.55 | 0.64 | -10.6 | 21.7 | 0.85 | 0.33 | -3.8 | 16.4 | 0.79 | 0.41 | No |
3 | 0 | 7.5 | 0.66 | 0.47 | -11.2 | 15.9 | 0.88 | 0.4 | -3.5 | 12.1 | 0.69 | 0.53 | Yes |
|
0 | 6.8 | 0.45 | 0.79 | 0.7 | 19.9 | 1.67 | 0.19 | 1.6 | 17.8 | 1.36 | 0.28 | No |
|
0 | 10.2 | 0.57 | 0.63 | -3.3 | 18.6 | 0.77 | 0.22 | -0.6 | 16.1 | 0.77 | 0.5 | Yes |
6 | 0 | 14.7 | 0.99 | 0.3 | -11.5 | 19.9 | 0.97 | 0.17 | -12.9 | 18 | 1.08 | 0.24 | No |
7 | 0 | 20.2 | 0.51 | 0.76 | 9.7 | 27.7 | 1.14 | 0.2 | -2.2 | 37.3 | 1.38 | 0.2 | No |
|
0 | 6.4 | 0.51 | 0.78 | -11.8 | 25.2 | 0.83 | 0.23 | -7 | 17.2 | 0.66 | 0.6 | Yes |
|
0 | 14 | 0.57 | 0.68 | -24.5 | 30.6 | 1.29 | 0.24 | -11.3 | 25.7 | 0.9 | 0.3 | No |
|
0 | 15 | 0.58 | 0.51 | -32.5 | 39.4 | 1.19 | 0.27 | -17.3 | 33 | 0.91 | 0.33 | No |
|
0 | 38.5 | 0.64 | 0.46 | -15.6 | 51.7 | 0.93 | 0.29 | -0.6 | 51 | 0.93 | 0.35 | No |
|
0 | 9.2 | 0.7 | 0.54 | 3.3 | 11.7 | 0.86 | 0.2 | -0.2 | 12.4 | 0.88 | 0.27 | No |
|
0 | 20.5 | 0.75 | 0.35 | 10.7 | 19.9 | 0.72 | 0.27 | 7 | 15.8 | 0.69 | 0.41 | Yes |
|
0 | 19.3 | 0.69 | 0.58 | -21.3 | 27.7 | 1.21 | 0.2 | -16.5 | 21.7 | 1.05 | 0.39 | No |
|
0 | 33.3 | 0.88 | 0.03 | -7.9 | 27.2 | 0.9 | 0.36 | -12.6 | 29.5 | 0.99 | 0.33 | No |
|
0 | 9 | 0.71 | 0.04 | 7.1 | 14.6 | 0.63 | 0.22 | 1.2 | 12.9 | 0.51 | 0.58 | Yes |
|
0 | 37.5 | 0.45 | 0.86 | 13.4 | 91 | 1.51 | 0.39 | 9.8 | 85.4 | 1.37 | 0.17 | No |
|
0 | 19.9 | 0.7 | 0.33 | -13.6 | 21.4 | 1.01 | 0.18 | -9.7 | 15.9 | 0.84 | 0.44 | Yes |
|
0 | 14.8 | 0.55 | 0.65 | -5.8 | 16.2 | 0.74 | 0.37 | 2 | 16.6 | 0.69 | 0.43 | Yes |
|
0 | 10.3 | 0.56 | 0.78 | -3.4 | 17.1 | 0.88 | 0.27 | -5.4 | 17.2 | 0.96 | 0.39 | No |
Mean | 0 | 16.5 | 0.62 | 0.55 | -6.1 | 27.6 | 1.01 | 0.25 | -3.8 | 25.6 | 0.94 | 0.37 | Criteria |
Stdev | 0 | 9.7 | 0.14 | 0.24 | 12.4 | 17.7 | 0.27 | 0.09 | 7.7 | 17.5 | 0.26 | 0.12 | Pas sing |
For cases meeting the criteria | Rate | ||||||||||||
Mean | 0 | 12.6 | 0.64 | 0.47 | -4 | 18.8 | 0.8 | 0.27 | -1.5 | 15.2 | 0.69 | 0.5 | |
35% | |||||||||||||
Stdev | 0 | 5.8 | 0.09 | 0.25 | 9.5 | 3.7 | 0.12 | 0.08 | 5.7 | 1.9 | 0.1 | 0.07 |
Subj+A3:R31ect | A | A | |||||||||||||||
|
|
||||||||||||||||
Training | Validation | Testing | Testing | Meeting | |||||||||||||
|
|
|
|
|
|
|
Criteria | ||||||||||
1 | -1 | 14.9 | 0.6 | 0.6 | #VALUE | 17.3 | 0.8 | 0.42 | 7.9 | 24.3 | 0.74 | 0.4 | 10.3 | 23.4 | 0.77 | 0.4 | No |
2 | -1.1 | 12.1 | 0.6 | 0.6 | -2 | 12.7 | 0.57 | 0.63 | 7.7 | 17.6 | 0.65 | 0.54 | 1.6 | 11.9 | 0.54 | 0.7 | Yes |
3 | -2.8 | 8.6 | 0.6 | 0.6 | -2.5 | 11.3 | 0.64 | 0.57 | 13.1 | 15.7 | 0.94 | 0.45 | 2.1 | 10.7 | 0.65 | 0.6 | Yes |
4 | -0.8 | 9 | 0.7 | 0.4 | 0.6 | 7.8 | 0.71 | 0.47 | 7.2 | 11.1 | 0.93 | 0.32 | 6.8 | 9.8 | 0.73 | 0.5 | Yes |
5 | 2.9 | 16.1 | 0.6 | 0.5 | -4.2 | 18.8 | 0.71 | 0.37 | 1.6 | 15.6 | 0.75 | 0.33 | -2.1 | 13.4 | 0.72 | 0.5 | Yes |
6 | -0.5 | 17.2 | 0.7 | 0.5 | -10.1 | 14.7 | 1.1 | 0.36 | -7.8 | 15.8 | 0.81 | 0.5 | -7.3 | 15 | 0.93 | 0.3 | No |
7 | 0.3 | 25.2 | 0.7 | 0.4 | 1.9 | 13.7 | 0.6 | 0.52 | 2.6 | 15.1 | 0.71 | 0.51 | 0 | 23 | 0.84 | 0.2 | No |
8 | 0 | 13.7 | 0.7 | 0.4 | 6.1 | 23.6 | 0.71 | 0.44 | 0 | 22 | 0.72 | 0.4 | -3.9 | 16.5 | 0.61 | 0.6 | Yes |
9 | 0.2 | 16.3 | 0.7 | 0.6 | -2.8 | 14.4 | 0.7 | 0.68 | -0.3 | 18.6 | 0.7 | 0.49 | 7.4 | 22.9 | 0.72 | 0.4 | No |
10 | 1.3 | 15.2 | 0.4 | 0.8 | -4.8 | 23.2 | 0.69 | 0.49 | -7.9 | 24.1 | 0.69 | 0.53 | 8.4 | 28.9 | 0.78 | 0.4 | No |
11 | 0 | 42.3 | 0.7 | 0.6 | -16.1 | 37.8 | 0.97 | 0.54 | -24 | 45.3 | 0.8 | 0.43 | -3.8 | 41.2 | 0.7 | 0.5 | Yes |
12 | 0 | 8.7 | 0.6 | 0.4 | 9.7 | 15.5 | 1.01 | 0.29 | 3.6 | 11.2 | 0.89 | 0.27 | 0.4 | 10.7 | 0.9 | 0.5 | Yes |
13 | 3.1 | 19.1 | 0.9 | 0.5 | 14.5 | 19.8 | 1.3 | 0.53 | 16.9 | 24.4 | 0.72 | 0.52 | 6.9 | 21.4 | 0.8 | 0.4 | No |
14 | -1.1 | 14.4 | 0.5 | 0.7 | -7.6 | 17 | 0.83 | 0.43 | -7.6 | 18 | 0.77 | 0.53 | -12 | 20.1 | 0.94 | 0.4 | No |
15 | 0.3 | 21 | 0.8 | 0.4 | 21.1 | 24.3 | 1.01 | 0.45 | 0.7 | 23.3 | 0.68 | 0.43 | -0.9 | 20.3 | 0.66 | 0.5 | Yes |
16 | -0.2 | 21.4 | 0.7 | 0.4 | -26.1 | 26.1 | 1.68 | 0.52 | -24 | 25.1 | 1.56 | 0.42 | 0.2 | 13 | 0.85 | 0.4 | Yes |
17 | 4.4 | 51.9 | 0.6 | 0.6 | -4.5 | 36.1 | 0.66 | 0.59 | 16.6 | 41.1 | 0.73 | 0.59 | -5.5 | 47.6 | 0.73 | 0.5 | No |
18 | 0.1 | 13 | 0.6 | 0.7 | 8.5 | 14.8 | 0.64 | 0.63 | -5.4 | 18.8 | 0.95 | 0.33 | -0.6 | 13.3 | 0.75 | 0.5 | Yes |
19 | -9.2 | 14.9 | 0.7 | 0.6 | -4.3 | 16.1 | 0.65 | 0.5 | -5.7 | 19.7 | 0.9 | 0.14 | 0.7 | 17.9 | 0.74 | 0.5 | No |
20 | 0 | 13.9 | 0.6 | 0.6 | -3.7 | 11 | 0.78 | 0.43 | -12 | 16.9 | 0.98 | 0.38 | -9.6 | 14.7 | 0.85 | 0.5 | Yes |
Mean | -0.2 | 18.4 | 0.7 | 0.6 | -1.6 | 18.8 | 0.84 | 0.49 | -0.9 | 21.2 | 0.83 | 0.42 | 0 | 19.8 | 0.76 | 0.5 | Criteria |
Stdev | 2.7 | 10.8 | 0.1 | 0.1 | 10.4 | 7.8 | 28 | 0.1 | 11.4 | 8.6 | 20 | 0.11 | 6 | 9.9 | 0.11 | 0.1 | Passing |
For cases fleeting the criteria | |||||||||||||||||
Mean | -0.2 | 12.9 | 0.6 | 0.5 | 3.8 | 15.5 0.75 0.47 | 16.9 | 0.83 | 0.38 | -0.7 | 13.5 | 0.71 | 0.55 | ||||
Stdev | 1.5 | 4 | 0.1 | 0.1 | 8.4 | 5.7 0.16 0.12 | 4.2 | 0.13 | 0.08 | 4.5 | 3.3 | 0.11 | 0.08 | 55% |
Subject | , | A Yt | |||||||||||||||
Tit * | |||||||||||||||||
Training | Validation | Testiig | Testing | Meeting | |||||||||||||
AE I AAE I RAAEI rfit | AE I AAE | RAAEI rfit | AE I AAE I RAAEI rfit | AEI AAE IRAAEI rat | criteria | ||||||||||||
1 | 1.7 | 16.2 | 0.72 | 0.47 | 14.6 | 30.3 | 0.79 | 0.47 | 11.9 | 19.5 | 0.75 | 0.42 | 17.5 | 24.7 | 0.82 | 0.33 | No |
0.4 | 11.6 | 0.56 | 0.66 | 12.6 | 19.2 | 0.71 | 0.36 | 7.6 | 173 | 0.64 | 0.7 | 0.2 | 10.3 | 0.5 | 0.78 | Yes | |
3 | -1.8 | 10 | 0.61 | 0.59 | 12.5 | 17.4 | 1.08 | 0.29 | 7.2 | 11.1 | 0.64 | 0.62 | -0.2 | 10.1 | 0.74 | 0.46 | Yes |
4 | -0.5 | 83 | 0.7 | 0.45 | 5.8 | 11.4 | 0.9 | 0.18 | 7.7 | 10.2 | 0.9 | 0.5 | 6.2 | 9.9 | 0.68 | 0.5 | Yes |
5 | 6.7 | 17.6 | 0.68 | 0.41 | 9.2 | 14.8 | 0.74 | 0.49 | 9.6 | 17.9 | 0.82 | 0.28 | -1.5 | 14.1 | 0.74 | 0.48 | Yes |
6 | -3.7 | 16.1 | 0.8 | 0.41 | -6.2 | 13.8 | 0.69 | 0.63 | -5.5 | 143 | 0.74 | 0.53 | -2.8 | 13 | 0.77 | 0.41 | Yes |
7 | -2.3 | 22 | 0.7 | 0.43 | 3.1 | 14.5 | 0.57 | 0.53 | 1.2 | 12.9 | 0.65 | 0.55 | 3.2 | 20.3 | 0.8 | 0.25 | No |
8 | 2.5 | 18.4 | 0.67 | 0.45 | -2.7 | 20.4 | 0.7 | 0.44 | -0.2 | 22.7 | 0.71 | 0.42 | -7.8 | 17.9 | 0.7 | 0.56 | Yes |
9 | 0.7 | 14 | 0.62 | 0.61 | 2.5 | 18.5 | 0.88 | 0.36 | 3.4 | 212 | 0.69 | 0.59 | 8.5 | 22.3 | 0.69 | 0.49 | Yes |
10 | -5.1 | 19.7 | 0.55 | 0.66 | -10.5 | 23.4 | 0.81 | 0.44 | -11.5 | 26.7 | 0.67 | 0.58 | 3 | 29.7 | 0.78 | 0.41 | No |
11 | -2.6 | 35.7 | 0.65 | 0.51 | -9.1 | 30 | 0.57 | 0.58 | -28.7 | 503 | 0.86 | 0.49 | 6.5 | 38.9 | 0.61 | 0.62 | Yes |
12 | 0.8 | 123 | 0.85 | 0.1 | 3.3 | 11.3 | 0.85 | 0.27 | -3.1 | 8.9 | 0.74 | 0.21 | 1.3 | 8.9 | 0.88 | 0.46 | Yes |
13 | 9.1 | 17 | 0.9 | 0.54 | 21.3 | 23 | 0.84 | 0.56 | 12.8 | 23.8 | 0.59 | 0.57 | 7.4 | 17.7 | 0.64 | 0.38 | Yes |
14 | -2.9 | 152 | 0.62 | 0.64 | -7.6 | 15.9 | 0.69 | 0.64 | -6.4 | 183 | 0.81 | 0.4 | -11.9 | 20.7 | 1.04 | 0.33 | No |
15 | 10.1 | 212 | 0.78 | 0.48 | 6.2 | 22.6 | 0.69 | 0.62 | -4.7 | 23 | 0.65 | 0.51 | -10.3 | 23.7 | 0.75 | 0.44 | No |
16 | 9.9 | 18.1 | 0.73 | 0.27 | -2.7 | 16.4 | 0.85 | 0.26 | -4.4 | 7.7 | 1.12 | 0.26 | 3.9 | 9 | 1.09 | 0.43 | Yes |
17 | 2.3 | 48.1 | 0.69 | 0.67 | 3.5 | 39.8 | 0.76 | 0.58 | 26.9 | 45.9 | 0.76 | 0.67 | 3.4 | 48.8 | 0.8 | 0.42 | No |
18 | 1.3 | 122 | 0.52 | 0.69 | -9 | 18.5 | 0.9 | 0.46 | -9.3 | 193 | 1.03 | 0.25 | -0.8 | 14.3 | 0.82 | 0.46 | Yes |
19 | -1 | 18.7 | 0.81 | 0.28 | 2.3 | 16.7 | 1.06 | 0.28 | -0.8 | 25.9 | 0.98 | 0.15 | -5.8 | 21.3 | 0.78 | 0.46 | No |
20 | 6.5 | 132 | 0.65 | 0.59 | -3.7 | 12.1 | 0.71 | 0.58 | -4.4 | 16.6 | 0.93 | 0.21 | -5.6 | 12.7 | 0.81 | 0.53 | Yes |
Mean | 1.6 | 183 | 0.69 | 0.5 | 2.3 | 19.5 | 0.79 | 0.45 | 0.5 | 20.7 | 0.78 | 0.45 | 0.7 | 19.4 | 0.77 | 0.47 | Criteria Passing Rate |
Stdev | 4.6 | 9.1 | 0.1 | 0.15 | 8.8 | 7.2 | 0.14 | 0.14 | 11.4 | 10.9 | 0.15 | 0.17 | 7 | 10.3 | 0.13 | 0.11 | |
For cases meeting the criteria | |||||||||||||||||
Mean | 3.1 | 0.2 | 0.7 | 0.46 | 4.7 | 17.6 | 0.79 | 0.4 | 0.4 | 18.7 | 0.S0 | 0.43 | 1.1 | 15 | 0.74 | 0 .54 | |
162 | |||||||||||||||||
4.6 | 7.7 | 0.11 | 0.17 | 9.4 | 5.9 | 0.14 | 0.15 | 12 | 12.5 | 0.16 | 0.18 | 5.1 | 9.1 | 0.16 | 0.1 | 65% |
We found that using the armband inputs increases
This article presented preliminary work on the development of a virtual sensor for BGC with the objective of developing a noninvasive CGM system that could increase CGM among non-insulin dependent people. This device would require users to wear a readily available armband monitor and manually entering meal sizes through the use of a button on the armband. This device would require four (4) lancet measurements per day as most current invasive CGMSs require.
The modeling methodology presented in this work is quite powerful. It takes on the challenge of modeling BCG in a highly complex, non-linear, multiple-input, highly underdetermined problem. As illustrated in this work, it is able to develop useful multiple-input dynamic models for BGC under free living, outpatient, data collection from just four glucose measurements per day and from as little as three days of data. In addition, these results are achieved with minimal food information of only three discrete levels. This ability stems from a number of innovative ideas to overcome several challenges in this complex modeling problem as follows. First, the use of the coupled structure allows for the inclusion of inferential blood insulin concentration and leads to insulin and glucose interaction in the blood. This structure is a significant advancement over a straight Wiener network and contributes significantly to the accuracy and ability to obtain adequate fitting for acceptable model usefulness. Secondly, the result in Appendix A provided the knowledge that produced the idea to decompose the modeling problem into a dynamic part and a static part. Added to this idea is the inspiration of determining the dynamic parameters for each input, one input at a time. Once the dynamic parameters are determined for each input, they are fixed. Note that, from the use of a validation set we are able to control over-fitting and by controlling
This work applied and improved the methodology from Rollins et al.
Future work will involve running clinical studies under the protocol that subjects will follow when wearing the device such as time stamping for meal size and using only their glucose meter to collect data. If these studies are successful, we plan to develop a prototype armband and evaluate it on several subjects. We envision this device collecting input and output data into the armband where the model will reside. After a sufficient number of lancet measurements have been collected, the model with be built from these data automatically for calibration of the device. After successful calibration, the armband will collect input data, infrequent output data, and display BGC continuously over time on a watch type display or smart phone. Transmission of data from the armband to the display monitor may utilize Bluetooth technology.
We have overcome many challenges such as the use of a food index, the lack of initial conditions, frequent and long term removal of the armband and multiple inputs, subject-specific, modeling under infrequent sampling. However, as this work is only preliminary, there are still several challenges to overcome. This includes finding novel ways to improve the accuracy that leads to a higher percent of users meeting the MAC. In addition, the model procedure is quite complex as it requires advanced modeling experience and consists of several steps. One way we plan to improve accuracy is by gaining a better understanding on the bounds of each parameter. To address the model identification issue, we plan to development an estimation algorithm that identifies parameters automatically. This program will reside in the armband and will be used to calibrate the virtual sensor from on-line data. These are areas of future research that we have begun and the results are quite promising.
The authors thank BodyMedia for funding much of the data collection and allowing us to use their equipment and Jeanne Stewart for assisting in data collection.
The purpose of this appendix is to provide a mathematical proof that
With
Thus, with