Sensors Based Optimized Closed Loop Control Algorithm to Minimize Hypoglycemia/Hyperglycemia using 4-Variate Time Series Data

Existing Artificial Pancreases system measures blood glucose concentration levels by extracting information from the CGM sensor, and based on the BGC, the control algorithm implemented in the controller automatically adjusts the insulin infusion rate of the automated insulin delivery system. The probable obstacles to executing an automatic insulin infusion engine contain hypoglycemia conditions, misunderstanding regarding suitable glycemic targets, various system, and procedural issues, and resistance to change. Insulin dosage, food intake, daily activities and lifestyle, and emotional states all have an impact on glucose variations in diabetic individuals. Our body discharges low, basal insulin to keep blood sugar levels under control overnight, fasting, and in the middle of suppertimes. A huge burst of insulin is released when you eat. This burst of insulin is required to eliminate all of the carbohydrates that your meal has taken something in. At mealtimes, a fast burst of insulin is released to manage blood glucose levels while eating. This mealtime insulin surges peak in around 45 minutes and then return to baseline/background levels. Because insulin stimulates glucose uptake by cells, this results in an inability to regulate normal blood glucose levels. Long-standing problems such as neuropathy, heart disease, and diabetes might occur if blood glucose levels continue to be high for a lengthier period. If it is left untreated, it causes Hyperglycaemia as well as chronic multiple organ impairment, cardiovascular disease, kidney failure, and blindness. To treat type 1 diabetes-related comorbidities, proper insulin therapy must be given to the patients at right time.

An AR model depends on only continuous blood glucose data of type-1 diabetic patients; the performance of parameter estimation was evaluated by using data-shooting and regularisation strategies to identify diabetic patients. However, in some studies exogenous (X) input variables can be used to include the special effects of insulin intake or carbohydrate intake on glucose, albeit the effect of carbohydrate intake on glucose is far less studied than the effect of insulin. ARMA models, ARMAX, and ARX models are developed for predicting the blood glucose levels in the existing literature survey [1].

Deep learning algorithms boost the performance of IoT- based healthcare applications dramatically. However, if the training values do not appropriately cover all working circumstances, CNN will be unable to extract useful features. However, it might be a difficult task during emergencies since data may not be available. The work create a new data-driven patients, taking into account the impact of prior glucose measurements, insulin, physical activity, and food intake. To estimate time-varying parameters and a state variable like glucose concentration at the same time, a recursive estimator based on extended Kalman filtering (EKF) is used. EKF also gives prediction covariance errors of glucose concentration and model parameters, which might be utilized to eliminate false hypoglycemia/hyperglycemia warnings and develop more robust control systems.

To eliminate frequent finger pricking, a CGM sensor is utilized to measure the diabetic patient's blood glucose level from the interstitial fluid. Because CGM sensors are implanted beneath the skin, they monitor interstitial glucose rather than blood glucose (BG).CGM sensors can be made "smart" by including algorithms that can send out notifications when glucose concentrations are expected to surpass normal range thresholds [19, 20]. To improve the signal-to-noise ratio (SNR) of CGM data, it must be filtered. There will be minor differences in measurement taken from the interstitial fluid and the blood samples, but it will be the same during the steady state phase.

The accelerometer sensor measures the user's current physical activity, such as sitting, sleeping, walking, jogging, and exercising. Based on the meal consumption, a biosensor is utilized to measure the carbs content. Because blood pressure, BMI, and heart rate have such close correlations, three additional sensors have been used to measure them.

3.1 6LoWPAN architecture

The 6LoWPAN standard enables efficient use of IPv6 at low power through related protocols. An adaptive layer of simple embedded node optimization can be done in low-cost wireless networks. Title Summary is required to operate an effective payload transmission. Also, fragmentation and rearrangement of both transfers should be grouped and layered. Therefore, the MAC network layer is introduced between the adaptive layers. The same IPv6 prefix is distributed by LoWPAN and routers across the LoWPAN node share network interface. The node first uses edge router registration to facilitate efficient network operation. These operations are part of Neighbour Discovery (ND).

1.png

Figure 1. 6LoWPAN architecture

However, most of the 6LoWPAN applications such as automatic meter reading and environmental monitoring have been developed using mesh topologies. As it is often covered and cost-effective for infrastructure, it adopts multi-hop forwarding to achieve energy efficiency. Such link-layer meshes, LoWPAN networks, and IPs are done in three different ways, including routing. Link-layer networks and mesh LoWPAN have transparent mesh-mesh transfers and are called the Internet Protocol.

3.2 Low-Power and Lossy Routing (LPLR) with 6LoWPAN

Routing is one of the primary network layer tasks defined in the Open Systems Interconnection (OSI) model. Various other tasks include resolving nodes and creating and maintaining network topologies. 6LoWPAN technology employs a modified IPv6 protocol stack for seamless connectivity. Consider a scalable network of M nodes, let N1, N2, and N3 be the coordinates of each node. A collection point (CP) is considered to be a cluster head at any physical location within it. The network interface of the node can reduce energy usage according to the following parameters.

a) NIC characteristics

b) Packet Size

c) Bandwidth usage

While the node is in listening mode and sleep mode, it assumes energy is being consumed; the power consumption is 1.0 W and 0.001 W respectively.

The transmitted energy and the Joule energy to the received packet are:

$E n_{\text {usage }}=\sum_{\mathrm{j}=1}^{\mathrm{p}} 5 * \operatorname{packetsize}(\mathrm{n}(\mathrm{j}))$     (1)

The lower value of convergence indicates a larger amount of data and the longer time required for training the algorithm. Each solution generates a random path with a maximum number of nodes between the source and destination and satisfies the following constraints.

$N_s \& N_d \leq N_{t h}$     (2)

where, $N_s$ and $N_d$, $\mathrm{s}$ is the source and destination node.

Then it will generate a random path with $N_i$ nodes, let the nodes in this path, $N P_{i+1}$. To evaluate the learning metric $M_p$ of each generated random path:

$M_p=\sum_{i=0}^{N_i} \frac{d_{i-1}}{E(i)}+L S_{i-1}$     (3)

Energy Level of each node $=E$

Link Support $L S_i$

The randomly generated path's learning metrics, i, is a positive integer that takes up the minimum value as two and the maximum value as the total number of nodes in that path, respectively. The $d_{i-1}$ distance between the successive nodes, $E(i)$, is the instantaneous energy of each node right from the source node and $L S_{i-1}$ is the link quality between the successive links in the path.

3.3 Sensor fusion using adaptive Kalman Filte

Let $\mathrm{x}_1, \mathrm{x}_2, \ldots \mathrm{x}_{\mathrm{n}}$ denote the sensor measurements from various sensors with covariance $\mathrm{w}_1, \mathrm{w}_2, \ldots \mathrm{w}_{\mathrm{n}}$ respectively. Each sensor processor $i$ supplies its prior estimates and covariances are $x_i^{\prime}\left(\frac{n+1}{n}\right), w_i^{\prime}\left(\frac{n+1}{n}\right), x_i^{\prime}\left(\frac{n+1}{n+1}\right)$, $w_i^{\prime}\left(\frac{n+1}{n+1}\right)$ where $\mathrm{i}=1,2 . . \mathrm{N}$. Fusion processor prior estimate is $x^{\prime}\left(\frac{n+1}{n}\right), w^{\prime}\left(\frac{n+1}{n}\right)$ and the fusion problem is to compute the total estimates and covariance matrix $w^{\prime}\left(\frac{n+1}{n+1}\right)$.

The Kalman Filter updates or corrects the prediction and the current state's uncertainty after receiving the measurement. The Kalman Filter also forecasts future states and so on. During the prediction step, the system state at the next time stamp is

$X_{n+1, n}^{\prime}=F X_{n, n}^{\prime}+G U_n+W_n$     (4)

where, $\mathrm{G}$ is the control matrix, $\mathrm{U}$ is the input variable, $\mathrm{W}$ is the process noise and $F$ is the state transition matrix. The prediction level of uncertainty is calculated by

$P_{n+1, n}=F P_{n, n} F^{\prime}+Q$     (5)

where, $Q$ is process noise uncertainty $Q_n=E\left(W_n W_n\right)^T$ Initial estimate: $\left(\mathrm{x}_{0,0}^{\prime}, \mathrm{P}_{0,0}\right)$.

During the update step, the Kalman Gain is.

Next, update the system state predicted at time $\mathrm{k}$ by the measured value

$X_{n, n}^{\prime}=X_{n, n-1}^{\prime}+K_n\left(Z_n-H X_{n, n-1}^{\prime}\right)$     (6)

where, output vector $\mathrm{Z}_{\mathrm{n}}=\mathrm{Hx}_{\mathrm{n}}$.

Finally, uncertainty will be updated based on the measurement is:

$P_{n, n}=\left(I-K_n H\right) P_{n, n-1}\left(I-k_n H\right)^T+K_n R_n K_n^T$      (7)

where, measurement uncertainty $R_n=E\left(V_n V_n\right)^T$ Total Daily Insulin Dose (TDID):

Generally, the total insulin required for a day will be calculated based on

$\text { Total daily insulin }=\frac{\text { weights in pounds }}{4}$     (8)

Carbohydrates coverage from the total daily insulin is calculated using the "500" rule by

CarbRatio $=\frac{500}{\text { TDID }}$     (9)

The $BG$ has been quantized into a predetermined number of classes to perform a classification of the events comparable to precise amounts of BG concentration. They are, Severe hyperglycemic, hyperglycemic, normal, hypoglycemic and severe hypoglycemic.

$\begin{gathered}

\text { Class set } C=\left\{\left(\text { if } \emptyset^{\prime}(t)<=50,\right.\right. \text { SHypo), } \\

\text { (if } 50>\emptyset^{\prime}(t)<=70, \text { Hypo), } \\

\text { (if } 70>\emptyset^{\prime}(t)<=180 \text {, Normal), } \\

\text { (if } 180>\emptyset^{\prime}(t)<=250, \text { Hyper), } \\

\text { (if } \left.\emptyset^{\prime}(t)>=250 \text {, SHyper) }\right\}

\end{gathered}$

where, denote the data as $\mathrm{D}_{\mathrm{i}}=\left[\mathrm{BG}_{\mathrm{i}}, \mathrm{HR}_{\mathrm{i}}, \mathrm{BPR}_{\mathrm{i}}, \mathrm{CHO}_{\mathrm{i}}, \mathrm{PH}_{\mathrm{i}}\right.$, $\left.\mathrm{IS}_{\mathrm{i}}, \mathrm{ID}_{\mathrm{i}}\right]$ where all these variables are calculated in the time series from 1 to $\mathrm{n} . \mathrm{BG}_{\mathrm{i}}=\left[\mathrm{BG}_1, \mathrm{BG}_2 \ldots . \mathrm{BG}_{\mathrm{n}}\right]$ is the blood glucose level, $\mathrm{HR}_{\mathrm{i}}$ is the heart rate, $\mathrm{BPR}_{\mathrm{i}}$ is the blood pressure rate, $\mathrm{IS}_{\mathrm{i}}$ insulin boluses, and $\mathrm{ID}_{\mathrm{i}}$ insulin diffusion rate. Typically, a blood glucose level of $180 \mathrm{mg} / \mathrm{dl}$ is typically considered the threshold for hyperglycemia. This value is widely acknowledged as the maximum limit for glucose levels after a meal. This value is crucial in establishing the desired ranges for maintaining glycemic control.

3.4 Estimation of insulin infusion rate from blood glucose concentration using time-varying state model

At time $t$, let $\varnothing^{\prime}(t)$ denote the measured blood glucose level, $x(t)$ denote the insulin delivered, $y(t)$ the carbohydrate being taken and $z(t)$ denotes the energy consumed due to physical activities at time $t$.

The measured blood glucose level at time $\mathrm{t}$:

$\phi^{\prime}(t)=\sigma(t)+n_1(t)$     (10)

$\sigma(\mathrm{t})$ is glucose concentration from interstitial fluid and $\mathrm{n} 1(\mathrm{t})$ is the measurement noise. Measured glucose concentration from the interstitial fluid at time $t+1$

$\sigma(t+1)=\mu_t[\sigma(t)]+I_t[X(t-u)]+M_t[X(t-v)]+\beta(t)$     (11)

$\mu[\sigma(t)]$ is the auto regressive value that denotes the blood glucose values at time $t+1, I_t[x(t-u)]$ is the dynamic linear regression of blood glucose values at time $t+1$ after insulin delivery with $u$ delay, $\mathrm{M}_{\mathrm{t}}[\mathrm{x}(\mathrm{t}-\mathrm{v})]$ is the dynamic linear regression of blood glucose values at time $t+1$ after meal intake with $v$ delay and $\beta(t)$ is the process noise.

$\mu_t[\sigma(t)]=\tau_1(t) \sigma(t)+\tau_2(t) \sigma(t-1)+\ldots+\tau_n(t) \sigma(t-n-1)$     (12)

$I_t[x(t-u)]=\phi_1(t) X(t-u)+\phi_2(t) X(t-u-1)+\ldots+\phi_h(t) X(t-u-(n-1))$      (13)

$M_1[X(t-v)]=\theta_1(t) X(t-v)+\theta_2(t) X(t-v-1)+\ldots+\theta_n(t) X(t-v-(n-1))$     (14)

$\tau_n(t)$ is the auto regressive coefficient, $\varphi_n(t)$ and $\theta_n(t)$ are the linear regression coefficients which are time varying coefficients. $\varphi_n$ will be considered negative because insulin intake always decreases the blood glucose concentration level whereas $\theta_{\mathrm{n}}$ will be assumed to be positive as carbohydrates always increase the blood glucose concentration level

$\left.\phi(t+1)=\frac{d}{d t}[\phi(t+1)+\phi(t)]+[e(t+1)-e(t)]+\left[p(t+1)-p(t)+X\left(t-d_1\right)\right]\right)$     (15)

where,

$\varnothing(t)$ and $\varnothing(t+1)$ is the blood glucose level at time $t$ and $t+1$.

$e(t)$ and $e(t+1)$ is the measurement noise at time $t$ and $t+1$.

$p(t)$ and $p(t+1)$ is the process noise at time $t$ and $t+1$ with zero mean and variance equal to $\sigma^2$.

The formula to determine the insulin dose for high blood glucose levels is:

Insulin dose for high blood glucose=Difference between actual blood sugar and target blood sugar $\div$ correction factor.

$I_h=\frac{\left(\phi^{\prime}(t)-T^{\prime}(t)\right)}{C F}$     (16)

The high blood sugar correction factor is calculated using the "1800" rule by the following formula:

Correction Factor $=\frac{1800}{\text { TDID }}$     (17)

where, TDID is the total daily insulin dose.

3.5 Carbohydrates prediction from the meals

The experiment will then be repeated for the entire day, with varying meal start times, maximum meal sizes, and delays. The projected rise in glucose content $G^{\prime}$ after meal consumption is compared to the observed glucose G". The rate of glucose production at time $t$ is related to the rate of carbohydrate consumption during the meal.

If $M_{s t}$ is the meal's start time, $M_{e t}$ is the meal's finish time, $M_{c g}$ is the meal's carbohydrate content in grams, and $M_d$ is the meal's duration, then $\mathrm{M}=\left[\mathrm{M}_{\mathrm{st}}, \mathrm{M}_{\mathrm{et}}, \mathrm{M}_{\mathrm{cg}}, \mathrm{M}_{\mathrm{d}}\right]$. The maximum meal duration is $\mathrm{M}_{\mathrm{m}}$, and the maximum meal size is $\mathrm{M}_{\mathrm{max}} ; \mathrm{d}$ is the maximum delay between the meal ingestion and the divergence of blood glucose into the circulation.

$G^{\prime}(t) \alpha y^{\prime}(t)$     (18)

$\left(G^{\prime}\left[t^{\prime}-t\right]\right)^{\prime}-\left(G^{\prime \prime}\left[t^{\prime}-t\right]\right)^{\prime}>\phi$     (19)

$d_{e u c}=\sqrt{\sum_i^t \frac{\left|G_p(i)-G_o(i)\right|^2}{t-M_{s t}}}$     (20)

Carbohydrate level at time $t$ is measured by:

$y^{\prime}(t)=\sum_{t=1}^n d_{\text {euc}}(t)+d_{\text {euc }}(t-1)+\ldots . .+d_{\text {euc }}(t-n-1)$     (21)

Using this formula, calculate the carbohydrate coverage insulin dose by:

$I_{C H O}=\frac{y^{\prime}(t)}{C H O \text { in grams inclined by } 1 \text { unit of insulin }}$     (22)

where, "CHO in grams inclined by 1 unit of insulin" differs based on the total daily insulin dose per day.

For example, if you eat 50 grams of carbohydrates for the breakfast, then the $\mathrm{CHO}$ insulin dose is calculated by: $50 / 10=5$ units. This means you need 5 units of insulin to maintain the blood glucose level due to carbohydrate inclination.

Total Insulin Dose $\mathrm{Ti}=\mathrm{I}_{\mathrm{h}}+\mathrm{I}_{\mathrm{CHO}}$     (23)

where, $\mathrm{I}_{\mathrm{CHO}}$ is the $\mathrm{CHO}$ insulin dose and $\mathrm{I}_{\mathrm{h}}$ is the Insulin dose for high blood glucose.

3.6 Continuous Glucose Monitoring (CGM) and energy consumption due to physical activities

Maintaining glycemic imbalance during and after physical activity usually necessitates additional carbohydrate intake and/or insulin cuts. If the physical activity duration is greater than 30 to 60 minutes then 10 to 15 grams of carbohydrates must be consumed to prevent hypoglycemia.

For the entire study participants were allowed to participate in physical activity, with examples including running, fitness center, and walking.

Energy spent due to physical activities is measured by:

$p y^{\prime}(t)=\frac{\sum_{t=1}^n p y(t)+p y(t-1)+\ldots+p y(t-n-1)}{n} * 100 \%$     (24)

The total insulin control action is based on:

$I S_{t+1}=\frac{K_n\left(I S(t-1)+\phi^{\prime}(t)+c^{\prime}(t)-p y^{\prime}(t)=e(t)\right)}{C F}-G R$     (25)

where, $\mathrm{K}_{\mathrm{n}}$ is the Kalman gain.

The equation you provided, Energy Consumption $=$ Power $x$ Time, is accurate. To determine the overall energy usage, one must multiply the power consumption of the system by the duration of its operation. This formula is widely used to calculate energy consumption. Need to guarantee the system's autonomy and maximise its utilisation time. The choice of energy system might be diverse. Low-power and energyefficient systems are generally sought for medical devices, particularly those designed for wear or implantation. This may entail the utilisation of batteries, energy harvesting methodologies (such as solar cells or motion harvesting), or even rechargeable systems, contingent upon the specific application. The specific energy system would rely on the power requirements of your gadgets and the required operational period between charging or maintenance.

3.7 Metrics to evaluate the prediction model

The model's prediction capability was computed on the full test dataset on hypoglycemia extremes (<70 mg/dl) and hyperglycaemic extremes (>180 mg/dl) cases and the mean absolute difference (MAD) is computed using Absolute Difference,

$A(t)=\frac{(\operatorname{CGM}(t) \text { predict }-\operatorname{CGM}(t) \text { actual })}{\operatorname{CGM}(\mathrm{t}) \text { actual }}$    (26)

Mean $A b s o l u t e$ Difference $\operatorname{MAD}(t)=\frac{A(t)}{N}$     (27)

$\operatorname{CGM}(\mathrm{t})_{\text {predict }}$ is the model's predicted glucose value at time $t$, and $\operatorname{CGM}_{\text {actual }}(t)$ is the actual CGM data value at time $t . N$ is the number of data points in the dataset.

Concerning the measured value, relative-absolute change RAC calculates the normalized absolute error between measurement and prediction.

$R A C=\frac{y_i-y^{\prime}}{y_i} * 100 \%$     (28)

The metric used to assess glucose prediction is temporal gain (TG), which represents the amount of average time gained for early identification of a probable hypo/hyperglycemia event using the model.

Temporal Gain $\left(T_{\mathrm{G}}\right)=(\mathrm{n}$-Delay $) * \mathrm{~s}(\mathrm{t})$

$\text { Delay }=\arg \min _{k \in[0,1]}\left\{\frac{1}{n-l} \sum_{i=1}^{n-l}\left(y_i-y^{\prime}\right)^2\right\}$     (29)

where, $\mathrm{n}$ is the number of samples in the dataset, $\mathrm{s}(\mathrm{t})$ is the sampling time.