Nonparametric glucose predictor

Abstract

A method for predicting future blood glucose concentrations for an individual patient includes identifying an individualized linear black-box model of glucose-insulin by estimating a plurality of impulse response functions, each of which describes the input-output relationship of a plurality of individualized patient data sets, where the impulse response functions are functions in a Reproducing Kernel Hilbert Space (RKHS), and applying linear prediction techniques to the selected model using the identified impulse response functions to obtain a predicted blood glucose concentration for the individual patient at a future time point.

Description

[Technical Field]

[0001] (Cross-reference to related applications) This application claims the benefits of U.S. Provisional Application No. 63 / 129,952, filed on 23 December 2020, which is incorporated herein by reference in its entirety. [Background technology]

[0002] Type 1 diabetes (T1D), an autoimmune metabolic disorder, is characterized by the destruction of pancreatic beta cells involved in insulin production. The resulting inability to produce insulin, a hormone crucial for glucose homeostasis, is associated with abnormally high blood glucose (BG) levels in the body. To maintain BG within a safe range, T1D patients need to administer insulin to themselves via external injection. High glucose levels in the body can lead to several complications over time, which can be caused by insufficient insulin administration. Conversely, hypoglycemia (BG below 70 mg / dL) represents an immediate threat to the patient's life and can be caused by over-treatment with insulin.

[0003] T1D management can be significantly improved by accurate prediction of future glucose levels, as well as by the design of specific alarm systems that can detect and prevent future critical situations. Another promising advance in T1D management is the so-called artificial pancreas (AP), which is a system that uses closed-loop control (CLC) algorithms to automatically adjust insulin injections, and several control algorithms for AP that leverage predictive models, including model predictive control (MPC), are referred to.

[0004] A key component of both predictive alert systems and APs is the mathematical model used to describe glucose dynamics, which must be able to handle the inter- and intra-subject variability of glucose responses to insulin and diet, which vary from person to person and change over time even within the same patient. This problem can be addressed by learning and updating patient-specific models of glucose-insulin dynamics and using them to design personalized predictive alert algorithms, or by personalizing the model-based CLC algorithm of the AP system. [Overview of the Initiative]

[0005] In one embodiment, a system and method are described herein for creating a patient-specific glucose-insulin system description that can be integrated, for example, into glucose prediction and control algorithms, using a black-box model learning algorithm. In some embodiments, linear time-invariant models are used. There are several advantages to the selection of such models. First, parameter estimation algorithms for this class of models have been extensively studied in this paper, making strong convergence results and statistical characterization available. Second, these models can be used to generate predictions simply by employing well-established and computationally convenient techniques such as Kalman filters. Third, they are well suited to model-based control schemes such as model predictive control (MPC) and provide computationally concise implementations. Finally, although metabolic physiology is nonlinear, various experiments (both in silico and in vivo) have shown that linear approximations can be sufficient to capture dynamic features essential for successful control design.

[0006] In addition to classical parametric models (ARX, ARMAX, ARIMAX, box-Jenkins method) identified using the prediction error method (PEM), in some embodiments, a newly emerging paradigm for linear black-box model identification, a non-parametric approach, may be used. This approach has been shown in preliminary evaluations to exhibit superior predictive performance compared to conventional identification methods for glucose-insulin data.

[0007] In further embodiments of the systems and techniques described herein, various degrees of freedom available in parametric approaches may be used to evaluate their effects. Specifically, comparisons are made between various system parameterizations, various model order selection criteria, and different parameter estimation methods. The evaluation of various model learning techniques is performed using a large experimental dataset collected from a population of 11 T1D individuals using the AP system 24 / 7 for 5 months. The results show that in some cases, nonparametric linear model learning provides a statistically significant improvement over the parametric approach.

[0008] In a particular embodiment, a method is provided for predicting the future blood glucose concentration of an individual patient. The method includes identifying a personalized linear black-box model of glucose-insulin by estimating a plurality of impulse response functions, each describing the input-output relationship of a plurality of personalized patient datasets, wherein the impulse response functions are functions in the regenerating nuclear Hilbert space (RKHS); and using the identified impulse response functions, applying a linear prediction technique to the selected model to obtain the predicted blood glucose concentration of the individual patient at a future point in time.

[0009] In one embodiment of this particular aspect, the linear prediction technique is a Kalman filter.

[0010] In another embodiment of this particular aspect, the individualized linear black box model is a time-invariant model.

[0011] In another embodiment of this particular aspect, the plurality of individualized input patient datasets includes a dataset of previous glucose levels over time for an individual patient, dietary intake data for the individual patient, and exogenous insulin delivered to the individual patient over time.

[0012] In another embodiment of this particular aspect, five pre-processings of the dietary intake data and the delivered exogenous insulin are performed to separate the dietary intake data from the delivered exogenous insulin so that the dietary intake data and the delivered exogenous insulin are not linearly dependent on each other.

[0013] In another embodiment of this particular aspect, the dataset of previous glucose levels over time for an individual patient is provided by a continuous glucose monitor.

[0014] In another embodiment of this particular aspect, a stable spline kernel is selected for the kernel of the RKHS.

[0015] In another embodiment of this particular aspect, the kernel hyperparameters are estimated using maximum marginal likelihood or cross-validation.

Brief Description of the Drawings

[0016] [Figure 1] It is a flowchart showing at a high level the steps included in the individualized model-based prediction method described herein. [Figure 2a] Respectively show the insulin input data signals before and after being transformed to reduce collinearity. [Figure 2b] Respectively show the insulin input data signals before and after being transformed to reduce collinearity. [Figure 3]For four different cases, the CondNum index (collinearity diagnosis) of the training set matrix that needs to be inverted for model identification is shown. [Figure 4] An example of the input training data after undergoing preprocessing is shown. [Figure 5a] For four different prediction ranges, the coefficient of determination metric (COD) for comparing parametric and non-parametric models is shown [Figure 5b] For four different prediction ranges, the coefficient of determination metric (COD) for comparing parametric and non-parametric models is shown [Figure 5c] For four different prediction ranges, the coefficient of determination metric (COD) for comparing parametric and non-parametric models is shown [Figure 5d] For four different prediction ranges, the coefficient of determination metric (COD) for comparing parametric and non-parametric models is shown [Figure 6a] The COD metric and the root mean squared error (RMSE) metric, which compare the performance achieved by a model with only CGM, a parametric model identified using insulin and dietary data, and a non-parametric model with inputs, are shown respectively [Figure 6b] The COD metric and the root mean squared error (RMSE) metric, which compare the performance achieved by a model with only CGM, a parametric model identified using insulin and dietary data, and a non-parametric model with inputs, are shown respectively [Modes for carrying out the invention]

[0017] I. Introduction Several different glucose-insulin models are proposed in this paper. According to a high-level classification, these models can be divided into white-box and black-box models. White-box models are based on a mechanistic / semi-mechanistic description of the physiological processes that occur in the metabolic system. Their complexity, i.e., the number of equations and model parameters, varies greatly depending on the model's purpose. "Minimal models" are concise approximations designed to ensure parameter identifiability under specific experimental conditions (e.g., oral glucose tolerance tests), while "maximum models" are large-scale models with several equations and parameters, primarily designed to simulate in silico tests. Both minimal and maximum physiological models present several problems when used for model-based glucose prediction or control. Minimal models are often too rigid to provide adequate data predictions, while maximum models are usually difficult to identify and therefore present limited effectiveness in dealing with intra-patient and inter-patient variability. Furthermore, physiological models are nonlinear, making their use in model-based computation and control algorithms for prediction difficult and often resulting in computationally expensive algorithms. For these reasons, significant effort has focused on investigating black-box models that are simply data-driven and do not describe any physiological processes. The literature on glucose mathematical models has so far proposed several data-driven approaches, either using classical linear models derived from system discrimination methods or nonlinear models obtained using machine learning (ML) strategies or deep learning (DL) techniques. Despite the consideration of several options, no algorithm has demonstrated a significantly superior performance compared to others in terms of predictive accuracy.

[0018] Figure 1 is a flowchart illustrating, at a high level, the steps involved in the personalized model-based prediction scheme described herein. As shown in the figure, the first step 10 of this scheme is to select a suitable model structure from among the various available options described above. In this case, the selected model is a personalized linear black-box model of glucose-insulin regulation. As described below, the selected model has model parameters that can be personalized from readily accessible patient logs, such as carbohydrate intake and insulin injection data, in order to mimic individual specific physiological functions.

[0019] In the second step 20 of the prediction scheme shown in Figure 1, selected model parameters to be personalized for individual patients are estimated using nonparametric estimation techniques. In one embodiment, the parameter estimation techniques used are a support vector regression approach, a Gaussian regression approach, and a Tikhonov regularization approach. Next, in the third step 30, the acquired personalized model is used in a prediction scheme based on a linear prediction method, such as a Kalman filter. II. Experimental Data A. Experimental Design

[0020] Data were collected during a multicenter clinical trial (www.clinicaltrials.gov:NCT02137512) aimed at evaluating the feasibility of a long-term closed-loop control (CLC) algorithm within an automated insulin delivery system, namely the Diabetes Assistant (DIAS) developed at the University of Virginia. The study and all experimental procedures were approved by each site's institutional review board or an independent review board and overseen by independent data monitoring and safety monitoring committees. Fourteen individuals with T1D participated in a five-month trial testing 24 / 7 use of the DIAS system. Glucose data were recorded with a 5-minute sample time using a DexCom G4 sensor (DexCom, Inc., San Diego, CA, USA), and insulin was injected using a Roche Accu-Check Spirit Combo insulin pump (Roche Diabetes Care, Inc., Indianapolis, IN, USA). These two off-the-shelf diabetes devices used low-energy Bluetooth to communicate with key system components, which are based on an Android-powered smartphone platform.

[0021] Further details regarding the data can be found in B. Kovatchevet al., "Feasibility of Long-Term Closed-Loop Control: A Multicenter 6-Month Trial of 24 / 7 Automated Insulin Delivery," Diabetes Technology and Therapeutics, vol.19, no.1, pp.18-24, 2017. For this purpose, several details regarding the treatment of T1D patients are highlighted below, and preferred notation is introduced.

[0022] The individual was instructed to manually deliver appropriate amounts of insulin for all meals by inserting all carbohydrate (CHO) intakes into the system. This manually recorded signal is referred to as the "meal signal" m(k). As far as insulin is concerned, at each time step k, the system injected an insulin dose i(k) that can be regarded as the sum of two components. i(k)=i ST (k)+Δi CL (k) Where, i ST (k) is the insulin prescribed by the standard T1D treatment for patients not using the AP system, and Δi CL (k) is the real-time insulin correction calculated by the CLC algorithm. The insulin i ST (k) can be further decomposed as i ST (k)=I b +i B (k), where I b is the amount of insulin to be injected to maintain stable BG during fasting (basal insulin, known as a segmented constant signal), and i B (k) is the insulin administered at meal times to mitigate the post-meal peak (known as the meal bolus). Specifically, at meal times,

Equation

[0023] Where, m(k) is the estimated CHO consumed, g(k) is the recorded glucose level, and G target is the BG target. ICR and CF are known as the insulin-to-carbohydrate ratio and correction factor, respectively. These two patient-specific numerical values suggested by the clinician indicate, respectively, how much insulin is required to cover a specific amount of carbohydrate and how much insulin is required to lower the BG by 1 mg / dL. Finally, the insulin on board iob(k) indicates how much insulin still remains in the body from the most recently delivered bolus.

[0024] i M (k) is known as the dietary bolus component and is intended to provide insulin coverage of ingested CHO, with the remaining portion i Corr (k) should be noted as a so-called corrective component, which includes manual insulin correction to compensate for high glucose levels at mealtimes or to take into account insulin still acting in the body. B. Data preprocessing

[0025] In this section, the inventors describe the test data, including insulin-related information i(k), carbohydrate intake m(k), and CGM-measured glucose g(k), without any missing values. s This shows a preprocessing step aimed at obtaining three signals that are equally sampled over a 5-minute period.

[0026] Glucose and insulin data were collected from different devices, and meals were manually recorded by the subjects; therefore, the relevant time series were slightly asynchronous and contained missing values.

[0027] To perform synchronization, all signals were aligned to the same time grid. Next, the inventors considered missing data. First, patients with more than 20% missing data were discarded, resulting in the exclusion of two subjects. For the remaining data, incomplete data portions longer than 30 minutes were discarded, and shorter gaps were interpolated. The interpolation strategy depended on whether the gaps occurred in the training or test data, as discussed below. Finally, consecutive 14-day data portions were searched for and found in the remaining patients, with one exception, resulting in a total of three excluded subjects.

[0028] For each of the 11 retained subjects, the previously identified 14-day data portion was split into two parts: the first 7 days were used for model training (training set), and the following 7 days were used to evaluate predictive performance on independent data (test set).

[0029] Both the insulin i(k) and diet m(k) signals are available in this configuration and strongly influence the BG level g(k). For this reason, we consider them as inputs to a model having glucose g(k) as its output. Furthermore, their physiological effects on glucose are quite different; insulin injection decreases BG, while the CHO assumption increases BG. This suggests that these two signals convey very different information, and therefore it is important to have both as inputs for accurate prediction of future BG levels. However, these two inputs are quite similar to each other, as shown in Figure 2a, because all CHO consumption is associated with an insulin bolus and is dominated by the diet-centered component (see Equation 2), and therefore is approximately linearly proportional to m(k). Intuitively, it is clear how this poses a major challenge to a black-box model learning approach, as in the training data, only instances exist where both signals increase simultaneously, making it difficult for the model learning method to infer the role of each input from the data without any physiological prior information. This fact has been previously noted and reported in relation to linear models. In statistical learning and system discrimination, this phenomenon is a known problem called input collinearity. More specifically, a key step in some discrimination procedures is the inversion of a matrix D constructed from training data, which in our case includes insulin and dietary values. Calculating the inversion of a matrix containing collinear signals is prone to large numerical errors. Collinearity can be quantified by the condition number CondNum(D) of this matrix, which is an index that measures how sensitive a function is to changes or errors in its inputs, and in our case, can be used as a diagnostic tool for collinearity.

[0030] The condition number D is,

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[0031] In our case, input collinearity may result in a matrix of poor conditions, which can lead to a very large CondNum and therefore a low-precision matrix inversion. To address this problem, in some embodiments, an input transformation may be used to mitigate collinearity, thereby separating two input signals while maintaining their interpretability. The new signals are defined as follows:

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[0032] The proposed transformation results in a significant reduction in the number of conditions of the matrix to be inverted in both parametric and nonparametric discrimination algorithms, thus demonstrating its effectiveness in reducing collinearity. Figure 3 shows the CondNum of the training set matrix that needs to be inverted for model discrimination in four different cases: with or without the new input transformation (at the most advanced average scale), with or without parametric discrimination techniques (parametric, P), or with nonparametric discrimination techniques (non-parametric, NP). As can be seen, the input transformation significantly reduces the CondNum, resulting in a better-conditioned inversion problem, and the inventors obtained improvements of approximately 80% and 87% using the parametric and nonparametric approaches, respectively.

[0033] In this case as well, for reasons of numerical stability, it is important to select measurement units such that the signal values ​​span a similar range. In our case, this is done using [g / min] and [U / hour] for diet and insulin information, respectively, and the CGM readings are expressed in [mg / dL]. Finally, according to the standard system identification pipeline, the glucose g(k) signal is scaled by mean scaling, i.e., its average:

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[0034] To avoid cumbersome notation, the preprocessed data used in the identification process is described below. * The terms are omitted and simply represented as g(k), i(k), and m(k). Finally, Figure 4 shows an example of the data, specifically the training set used to identify target #1 after the preprocessing steps described above.

[0035] This entire training set is available during model training, which is assumed to be performed retrospectively on previously collected patient data. Glucose prediction, on the other hand, should be performed in real time. Consequently, when predicting glucose at time k, it should not be assumed that the entire test set is known. Specifically, the sample mean of inputs and outputs calculated across the entire test set cannot be used as real-time preprocessing. Instead, in the above preprocessing, the inventors subtract the mean value of the signals calculated on the training set from both the training data and the test data.

[0036] Similarly, cubic spline interpolation was used to fill data gaps of less than 30 minutes in the training set, but this technique cannot be used on the test set because it is non-causal. Instead, zero-order hold was used on the test data because it is applicable in real time. III.Identification technology

[0037] As expected above, one aspect of the systems and techniques described herein identifies a linear time-invariant black-box multi-input-single-output (MISO) model having (converted) insulin i(k) and dietary information m(k) as inputs and glucose level g(k) as an output. This corresponds to identifying the system transfer function, or equivalently, the system impulse response. To do so, two different approaches, a parametric strategy and a nonparametric strategy, are considered. A. Parametric approach

[0038] The parametric approach restricts the search for system dynamics to a finite-dimensional set of transfer functions parameterized by parameter vectors.

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[0039] Therefore, the first degree of freedom in a parametric discrimination pipeline is the selection of a suitable model class, and in this study, the inventors considered all the options listed above. Another choice that must be addressed in a discrimination pipeline is model complexity, i.e., the number of parameters that must be estimated (model order). The details of this step are described below.

[0040] Finally, the model parameters must be estimated, and the most advanced approach is the Prediction Error Method (PEM), where the parameter vector is the relevant predictor.

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[0041] Model order selection is performed considering two well-known reduction criteria: the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). Furthermore, for this task, the inventors also performed 7-fold cross-validation (CV), dividing the data into 7 complementary subsets for each round of CV, training the model using 6 days of data, and evaluating model performance using the remaining days.

[0042] It should be noted that investigating all possible combinations of degrees would have resulted in a computationally impractical analysis; in fact, preliminary studies on in silico populations or real-world data have shown that systematic investigations yield only very slight improvements in predictive accuracy. For this reason, the inventors ensured that all polynomial degrees were equal. Degrees in the range of 1 to 20 were tested for ARX, ARMAX, and ARIMAX parameterizations, while degrees in the range of 1 to 15 were tested using the BJ model.

[0043] The two delays correspond to physiological values ​​of 45 minutes and 15 minutes, i.e., n k1 = 9 steps and n k2 = Fixed at 3 steps. B. Nonparametric Approach

[0044] Here, we can assume that the predictor one step ahead can be written as follows.

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[0045] Furthermore, from (Equation 12), the covariances of the impulse responses h1, h2, and h3 are, respectively, the parameters

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[0046] In the formula, I n is the n×n identity matrix. Regarding the hyperparameters (denoted by ζ), the inventors estimated them via the maximum limiting likelihood.

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[0047] The nonparametric approach was implemented in two different ways. On the one hand, the inventors considered Matlab built-in functions. This option treats the problem as a regularized parametric approach, considering very high-order models to avoid overfitting and adding a regularization term representing a suitable prior distribution for unknown coefficients to the standard PEM cost function. As a suitable prior distribution, the inventors adopted a stable spline kernel. On the other hand, all the clauses presented by the inventors were implemented ad hoc. IV. Evaluation Metrics

[0048] To evaluate the predictive accuracy of the identified models, the inventors compared predictions of future CGM values ​​with their actual measured values, considering different prediction ranges (PH).

[0049] The model's predictions for the next PH step, i.e., predictions obtained by using past glucose values ​​up to time k-PH, g(k-PH), g(k-PH-1), ..., and inputs up to time k, i(k), i(k-1), ..., m(k), m(k-1), ...,

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[0050] Furthermore, the inventors considered the time gain (TG) given by the prediction as follows. TG(PH) = PH - delay(PH), In the formula, the delay between the original profile and the predicted profile is quantified by the temporal shift τ that maximizes the cross-correlation (crossCorr), which is a measure of similarity between g and the shifted version of g.

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[0051] Analysis of variance (ANOVA) was performed to compare accuracy metrics between different complexity criteria. When one of the analyzed distributions was found to be non-normal by the Lilliefors test, the Kruskal-Wallis test was used instead of ANOVA. Paired t-tests were performed to compare parametric and non-parametric models.

[0052] All reported p-values ​​are two-sided and are considered statistically significant when <0.05. V. Results

[0053] Starting with a parametric approach, the first degree of freedom to evaluate is the choice of model order. Table 1 reports the predictive performance of various order selection criteria for all classes of parametric models. Specifically, the median RMSE and interquartile range (IQR) are reported for different prediction ranges (PH).

[0054] In addition to considering patient-specific model complexity achieved by individualizing the model order using AIC, BIC, or CV, Table 1 also considers the use of population order (PopOrd) for all patients: model complexity is not individualized, but model parameters are individually unique. This option accelerates model identification in the subject by eliminating the model order selection step.

[0055] No significant differences were found between the complexity methods considered. This is consistent with the results of comparing the same degrees of freedom using simulation data. Considering this, the inventors decided to use Population Order (PopOrd) for the remainder of the analysis. Table 1 also shows the median and IQR of the selected orders, with BIC selecting the lowest order and CV selecting the highest order, as BIC is expected to be one of the most conservative attenuation criteria. Population Order (PopOrd) provides a trade-off between these two ends. [Table 1]

[0056] Table II reports the predictive performance of all considered models for a 60-minute forecast range. All considerations derived in this case remain valid for other forecast ranges presented in Table IV. For baseline comparison, in addition to the individualized models obtained using parametric and nonparametric approaches, the inventors also report the performance of a collective model, i.e., a universal model identified on all subject data using parametric and nonparametric approaches. [Table 2]

[0057] The first point, as shown in Table II, is that parametric population predictors systematically outperform their individualized counterparts. The best median RMSE achieved by population models is approximately 34.1 mg / dL, while for individualized models, the RMSE is consistently lower than 32 mg / dL. This confirms that inter-patient variability significantly impacts the effectiveness of population models.

[0058] Comparing parametric models with respect to parameter estimation methods, we find that predictors identified by minimizing the 60-minute prediction error achieve similar or slightly worse performance compared to models selected using PEM. This is consistent with the theory that PEM is optimal in a suitable statistical sense.

[0059] Regarding the model class and the last degree of freedom of the parametric approach, consistent with previously obtained results, no significant differences in RMSE or COD were found among ARX, ARMAX, ARIMAX, or BJ. Nevertheless, BJ provides superior TG at a median of 20 minutes compared to the other model classes.

[0060] Finally, Table II shows that the best predictive performance is achieved by a nonparametric approach, specifically by an ad-hoc implementation achieving a median RMSE of approximately 29.8 mg / dL and a median COD of approximately 57.4%. This implementation performs slightly better than the Matlab standard function. The improvement is achieved while providing the same time gain (median TG = 20 mins) as the most effective parametric model, the BJ model. This conclusion is further supported by Figures 5a–5d, which compare the parametric model (specifically BJ) with the nonparametric model (ad-hoc implementation). The top panel of the figures reports box plots of COD achieved by the two methods in populations with PH = 30, 60, 90, and 120 mins. The nonparametric model provides COD improvements of approximately 2%, 7%, 21%, and 41% for PH = 30, 60, 90, and 120 mins, respectively. The lower panel of each figure reports ΔCOD, i.e., the difference between the COD achieved by the nonparametric model for a single patient and the COD derived from the parametric model for the same patient. Notably, these plots show a positive difference for the vast majority of subjects, meaning that the improvement in prediction is achieved not only on average but also for the majority of the subjects. Paired sample t-tests confirm that predictive accuracy differs significantly for PH=30, 60, and 90 minutes (p-value ≤ 0.001, p-value = 0.003, and p-value = 0.03, respectively), while for PH=120 minutes, the p-value is 0.07. [Table 3]

[0061] In some embodiments, the systems and techniques described herein relate to the derivation of patient-specific models of glucose-insulin interactions for personalized glucose prediction and personalized automated glucose control. With this in mind, the inventors focused on a systematic analysis of linear data-driven model learning techniques, as linear approaches have several advantages for prediction and control as previously discussed. Nevertheless, one might question whether patient physiological functions are nonlinear and therefore whether employing a nonlinear data-driven approach has the potential to significantly improve glucose prediction. As a preliminary investigation of this issue, three state-of-the-art deep-learning (DL) architectures for generating nonlinear models were implemented. The aim of this analysis is not a comprehensive investigation of these techniques and associated degrees of freedom, but merely to find out whether, using the same amount of data, these techniques offer significantly different performance compared to the techniques considered in this study. Specifically, the inventors investigated two different recurrent neural network (RNN) architectures that implement feedback connections to capture temporal dependencies in sequential data: long-short-term memory (LSTM) and gated recurring unit (GRU). Furthermore, the inventors implemented a temporal convolutional network (TCN) that uses convolutional operations, which are more effective in capturing local information along with temporal information compared to RNNs. With regard to linear techniques, the DL method was used both to derive a population model identified using all available data and to train a patient-specific model using only data for a particular subject. Table III presents a comparison of the performance achieved in terms of RMSE for different PHs.

[0062] Compared to linear strategies, nonlinear DL techniques achieve better performance using population models, likely because they require larger datasets to accurately estimate their parameters. Furthermore, their structures are highly flexible, thus likely to handle inter-patient variability internally to some extent. Nevertheless, none of these DL approaches perform significantly better than linear models; in fact, they achieve slightly worse performance for each PH compared to the proposed linear nonparametric method. This preliminary analysis does not rule out the possibility that other DL or nonlinear machine learning algorithms may perform better than the proposed linear black-box technique, but it demonstrates that the linear assumption is a viable alternative for more complex models.

[0063] With respect to other (linear and nonlinear) methods, our findings are comparable to or slightly better in terms of predictive accuracy. However, it should be noted that comparisons of literature studies based solely on numerical results can be misleading due to the use of different datasets, preprocessing techniques, and evaluation metrics.

[0064] We tested different versions of the nonparametric approach using Gaussian processes or kernel-based adaptive filters, obtaining results consistent with our findings. Nevertheless, the stable spline kernel used herein is specifically designed to enhance the stability of the predictor's impulse response, a key feature for control purposes.

[0065] To avoid the need to collect glucose, insulin, and dietary data simultaneously and synchronously, several contributions in this literature have attempted to avoid the use of any additional signals by using different system identification, ML or DL ​​approaches using CGM-only data. However, the use of these additional signals has been shown to improve predictive performance, and this finding is also validated in this study. Specifically, Figures 6a and 6b compare the performance achieved by a CGM-only model, a parametric model identified using insulin and diet, and a nonparametric model with inputs. The median COD and RMSE across the populations of the prediction as a function of PH are reported in Figures 6a and 6b, respectively. As expected, including inputs improves the accuracy of predictions, especially for PHs greater than 45 minutes.

[0066] In this study, the inventors demonstrated that personalized models provide an effective tool for addressing inter-subject variability (inter-patient variability). These personalized models should also be continuously updated to track changes in patient physiological function over time (intra-patient variability). To achieve this, a recursive approach, in which the model is updated whenever new data arrives (e.g., every 5 minutes), was effectively used, as several contributions in this paper demonstrate.

[0067] While this is a well-established procedure for online model adaptation, for certain applications, less frequent model updates may be sufficient to track slow changes in patient dynamics. With this in mind, the inventors envision daily or weekly model updates achieved by performing offline identification procedures on previously collected patient data. This periodically repeated batch model identification can be performed using the algorithms investigated in this study without requiring any modifications to make them recursive.

[0068] Finally, we will describe the technical architecture of the system that runs the proposed algorithm. Artificial pancreas systems and advanced decision support systems that can benefit from personalized models are implemented on devices that can acquire CGM, diet, and insulin data, provide a viable graphical user interface, and are suitable for host (and potentially advanced) algorithms thanks to their significant computing power. An example of such a device is Diabetes Assistant (DIAS), a smartphone-based platform mentioned earlier in this study and adopted in several closed-loop trails. These systems also stream data to a remote server to enable remote patient monitoring. The batch model updates investigated in this paper can be performed on the aforementioned devices or moved to a remote server storing patient data, thus reducing local computational burden. Personalized and regularly updated models are a natural way to address the large in-subject and inter-subject variability in diabetes. They can be used to create accurate, patient-specific predictors of future glucose levels and design personalized control algorithms for more effective AP systems.

[0069] In summary, the embodiments of the systems and technologies described herein focused on linear data-driven technologies that utilize insulin and dietary information in conjunction with CGM data. Both parametric and nonparametric approaches, along with their respective degrees of freedom, were systematically investigated. Specific input transformations were applied to the inputs to mitigate input collinearity issues.

[0070] The results showed that personalized models performed better than their collective counterparts, thus demonstrating the importance of addressing inter-subject variability. Furthermore, the inventors showed that nonparametric approaches enable obtaining consistently more effective models across subjects, with relative improvements increasing as the prediction range increases. Preliminary comparisons showed that nonlinear data-driven techniques based on deep learning architectures did not perform better than linear model accuracy. The results confirmed that adding further information, such as CHO and injected insulin, provides a practically relevant improvement in predictive accuracy for PH beyond 45 minutes.

[0071] The various operations of the methods described above can be performed by any suitable means capable of performing the operation, such as various hardware and / or software components, circuits, and / or modules. In general, any operation shown in the figures can be performed by the corresponding functional means capable of performing the operation.

[0072] The various exemplary logic blocks, modules, and circuits described in this disclosure may be implemented using general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate array signal (FPGAs) or other programmable logic devices (PLDs), discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but alternatively, a processor may be any commercially available processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors working with a DSP core, or any other such configuration.

[0073] In one or more embodiments, the described functions may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, these functions may be stored or transmitted as one or more instructions or codes on a non-temporary computer-readable medium. Such non-temporary computer-readable medium may include, but not limited to, RAM, ROM, EEPROM, CD-ROM, or other optical disk storage devices, magnetic disk storage devices, or other magnetic storage devices.

[0074] The methods disclosed herein include one or more steps or actions to achieve the described method. The method steps and / or actions may be interchangeable with one another without departing from the claims. In other words, unless a specific order of steps or actions is specified, the order and / or use of any particular steps and / or actions may be modified without departing from the claims.

[0075] Certain embodiments may include a computer program product for performing the operations described herein. For example, such a computer program product may include a computer-readable medium on which instructions that can be executed by one or more processors for performing the operations described herein are stored (and / or encoded). In certain embodiments, the computer program product may include packaging materials.

[0076] Furthermore, it should be understood that modules and / or other suitable means for performing the methods and techniques described herein may, where applicable, be downloaded and / or otherwise obtained by user terminals and / or base stations. For example, such devices may be coupled to a server to facilitate the transfer of means for performing the methods described herein. Alternatively, the various methods described herein may be provided via storage means (e.g., physical storage media such as RAM, ROM, compact discs (CDs), or floppy disks) so that the various methods can be obtained when user terminals and / or base stations couple or provide storage means to a device. Furthermore, any other suitable techniques for providing the methods and techniques described herein to a device may be utilized.

[0077] It should be understood that the claims are not limited to the exact configuration and components shown above. Various modifications, changes, and variations may be made to the configuration, operation, and details of the methods and apparatus described above without departing from the claims.

[0078] Unless otherwise defined, all terms (including technical and scientific terms) are given the usual, customary meanings to those skilled in the art and are not limited to any special or customized meanings unless expressly defined herein. It should be noted that the use of any particular term in describing a particular feature or aspect of the Disclosure should not be construed as implying that the term is redefined herein to be limited to any particular characteristic of the feature or aspect of the Disclosure to which it relates. In particular, in the appended claims, the terms and phrases used in this application, and their variations, should be construed as unrestrictive, as opposed to limited, unless otherwise specified.As mentioned above, the term "including" should be read as meaning "including, without limitation," "including but not limited to," etc., and the term "comprising" as used herein means "including," "containing," or "characterized by." The terms “have” are synonymous with “by)” and are comprehensive or unrestrictive, not excluding additional unlisted elements or method steps; the term “has” should be interpreted as “has at least”; the term “includes” should be interpreted as “includes but not limited to”; the term “examples” is used to provide exemplary cases of items in the consideration and is not an exhaustive or restrictive list thereof; adjectives such as “known,” “common,” “standard,” and similar terms should not be interpreted as limiting the items described to a given period or to items available at a given time, but rather to encompass known, common, or standard techniques that are available or may be known at any point in the present or future; the use of words such as “preferred,” “desired,” or “desirable,” and similar terms should not be understood as implying that certain features are critical, essential, or even more important to the structure or function of the invention, but rather as merely intended to highlight alternative or additional features that may or may not be utilized in particular embodiments of the invention. Similarly, a group of items connected by the conjunction "and" should not be interpreted as requiring each or all of those items to exist within the group, but rather, unless otherwise specified, should be interpreted as "and / or." Likewise, a group of items connected by the conjunction "or" should not be interpreted as requiring mutual exclusivity within the group, but rather, unless otherwise specified, should be interpreted as "and / or."

[0079] All numbers used herein to express quantities of components, reaction conditions, etc., are understood in all cases to be modified by the term "approximately." Therefore, unless otherwise indicated, numerical parameters described herein are approximations that may vary depending on the desired properties to be obtained. Each numerical parameter should be interpreted with regard to the number of significant figures and the usual rounding approach, at least not as an attempt to limit the application of the doctrine of equivalents to the scope of any claim in any application claiming priority to this application.

[0080] All references cited herein are incorporated herein by reference in their entirety. To the extent that any publications and patents or patent applications incorporated herein conflict with the disclosure contained herein, this specification is intended to supersede and / or take precedence over any such conflicting material.

[0081] Headings are included herein for reference and to help locate the various sections. These headings are not intended to limit the scope of the concepts described therein. Such concepts may be applicable throughout the specification.

[0082] Furthermore, although the foregoing has been described in some detail by examples and embodiments for the purpose of clarity and understanding, it will be apparent to those skilled in the art that certain changes and modifications may be made. Accordingly, the description and examples should not be construed as limiting the scope of the invention to the specific embodiments and examples described herein, but rather as encompassing all modifications and alternative forms that are associated with the true scope and spirit of the invention. [Table 4]

Claims

1. A method for predicting the future blood glucose concentration of an individual patient, performed by one or more processors, Identifying a personalized linear black-box model of glucose-insulin by estimating multiple impulse response functions that explain the input-output relationships of multiple personalized patient datasets, wherein the impulse response functions are functions in the regenerating nuclear Hilbert space (RKHS). This includes applying a linear prediction technique to the selected model using the identified impulse response function to obtain the predicted blood glucose concentration of the individual patient at a future point in time, The plurality of individualized patient datasets include a dataset of previous glucose levels over time for the individual patient, dietary intake data for the individual patient, and exogenous insulin delivered to the individual patient over time. The method further includes pre-treating the dietary intake data and the delivered exogenous insulin so that they are not linearly dependent on each other, thereby separating the dietary intake data from the delivered exogenous insulin. method.

2. The method according to claim 1, wherein the linear prediction technique is a Kalman filter.

3. The method according to claim 1, wherein the individualized linear black-box model is a time-invariant model.

4. The method according to claim 1, wherein the dataset of previous glucose levels over time for the individual patient is provided by a continuous glucose monitor.

5. The method according to claim 1, further comprising selecting a stable spline kernel for the kernel of the RKHS.

6. The method according to claim 5, further comprising estimating kernel hyperparameters using maximum limit likelihood or cross-validation.

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