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Neuronal networks are used in different fields of science and technology due to their capacity to approximate nonlinear functions through the synaptic weights optimization. This work shows a new form of optimization for neuronal networks based in fractional calculus. The fractional adaptation algorithm proposed was used to identify mechanical, electrical and biological systems. In each of the experiments a comparison between the proposed fractal-fractional model and the conventional model (with derivation order equal to one) was made.

In this work, a methodology based on a neural network to solve fractal-fractional differential equations with a nonsingular and nonlocal kernel is proposed, the neural network is optimized by the Levenberg–Marquardt algorithm. For evaluating the neural network, different chaotic oscillators of variable order are solved and compared with algorithms of numeric approximation.

In this work, we present a novel numerical method based on the fundamental theorem of fractional calculus and the Lagrange polynomial interpolation to solve numerically fractional delay differential equations. We focus on the fractional derivative with power-law, exponential decay and Mittag-Leffler kernel of Liouville-Caputo type with constant and variable-order. The numerical methods were applied to simulate the Duffing attractor, El-Nino/Southern-Oscillation, and Ikeda systems.

This study aims to assess the interoperability of Diabeloop’s DBLG1 Closed Loop System on glycemic control for T1D patients, based on data from clinical trials NCT02987556[1] (SP7) and NCT04190277 (SP8). SP7 study was conducted on 63 out of 68 patients randomly assigned to two arms equipped with DBLG1 system using Cellnovo pump for arm 1 and Kaleido pump for arm 2. All patients attended a 12-week open loop (OL) phase (receiving their usual treatment) and a 12-week closed loop (CL) phase (using DBLG1 system). In SP8 study, 178 out of 184 patients, randomly assigned to two arms, started with a 2-week baseline phase in OL. The next 12 weeks, patients in arm 2 remained in OL while patients in arm 1 switched to CL equipped with DBLG1 System using DANA Diabecare-i insulin pump. The study was shortened due to COVID-19 epidemic. To assess the improvement reached by DBLG1 System, we compared the average time in range 70-180 mg/dL (TIR) between OL and active CL phases. For SP7 study, we analysed data from both arms. For SP8 study, to assess the TIRs for the same patients, we compared baseline and CL phases for arm 1. As shown in Figure 1, for SP7 the average TIRs increased by 8.6% for arm 1 (32 patients) and by 14.0% for arm 2 (31 patients in CL, 30 in OL). For SP8 arm 1 the average TIR increased by 12.8% (142 patients). DBLG1 System improved the TIR despite the use of 3 different pumps. Therefore, improvement linked with DBLG1 System on the average TIR is independent of the pump used. Disclosure A. Adenis: Employee; Self; Diabeloop SA. L. Pou: Employee; Self; Diabeloop SA. H. M. Romero-ugalde: Employee; Self; Diabeloop SA. Y. Tourki: Employee; Self; Diabeloop SA. S. Franc: Advisory Panel; Self; Diabeloop SA, Board Member; Self; Novo Nordisk, Other Relationship; Self; Abbott Diabetes, Research Support; Self; Merck Sharp & Dohme Corp., Stock/Shareholder; Self; Diabeloop SA. G. Charpentier: Other Relationship; Self; Diabeloop. P. Y. Benhamou: Consultant; Self; Diabeloop SA, Eli Lilly and Company, Insulet Corporation, Other Relationship; Self; Abbott Diabetes. M. Doron: Research Support; Self; Diabeloop SA. E. Huneker: Employee; Self; Diabeloop SA.

This paper presents the simulation and control implementation on a Field Programmable Gate Array (FPGA) for a class of variable-order fractional chaotic systems by using sliding mode control strategy. Four different fractional variable-order chaotic systems via Atangana–Baleanu–Caputo fractional-order derivative were considered; Dadras, Aizawa, Thomas and 4 Wings attractors. A methodology has been developed to construct variable-order fractional chaotic systems using LabVIEW® software for its implementation in the National Instruments myRio-1900 (Xilinx FPGA Z-7010)® device. The variable-order fractional differential equations and the control law were solved using the variable-order Adams algorithm. Finally, simulation results show that FPGA provides high-speed realizations with the desired accuracy and demonstrate the effectiveness of the proposed sliding mode control.

In this paper, we approximate the solution of fractional differential equations using a new approach of artificial neural network. We consider fractional differential equations of variable-order with Mittag-Leffler kernel in Liouville–Caputo sense. With this new neural network approach, it is obtained an approximate solution of the fractional differential equation and this solution is optimized using the Levenberg–Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional differential equations, the Willamowski-Rossler oscillator and a multi-scroll system. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network different performance indices were calculated.

Objective Activity energy expenditure (EE) plays an important role in healthcare, therefore, accurate EE measures are required. Currently available reference EE acquisition methods, such as doubly labeled water and indirect calorimetry, are complex, expensive, uncomfortable, and/or difficult to apply on real time. To overcome these drawbacks, the goal of this paper is to propose a model for computing EE in real time (minute-by-minute) from heart rate and accelerometer signals. Approach The proposed model, which consists of an original branched model, uses heart rate signals for computing EE on moderate to vigorous physical activities and a linear combination of heart rate and counts per minute for computing EE on light to moderate physical activities. Model parameters were estimated from a given data set composed of 53 subjects performing 25 different physical activities (light-, moderate- and vigorous-intensity), and validated using leave-one-subject-out. A different database (semi-controlled in-city circuit), was used in order to validate the versatility of the proposed model. Comparisons are done versus linear and nonlinear models, which are also used for computing EE from accelerometer and/or HR signals. Main results The proposed piecewise model leads to more accurate EE estimations ([Formula: see text], [Formula: see text] and [Formula: see text] J kg-1 min-1 and [Formula: see text], [Formula: see text], and [Formula: see text] J kg-1 min-1 on each validation database). Significance This original approach, which is more conformable and less expensive than the reference methods, allows accurate EE estimations, in real time (minute-by-minute), during a large variety of physical activities. Therefore, this model may be used on applications such as computing the time that a given subject spent on light-intensity physical activities and on moderate to vigorous physical activities (binary classification accuracy of 0.8155).

Type 1 Diabetes is an autoimmune disease that eliminates endogenous insulin production. Without the crucial hormone insulin, which is necessary to equilibrate the blood glucose level, the patient must inject insulin subcutaneously. Treatment must be personalized (timing and size of insulin delivery) to achieve glycaemic equilibrium and avoid long-term comorbidities. Patients are educated on Functional Insulin Therapy (FIT) in order to independently adjust insulin delivery several times a day (at least prior to each meal and physical activity). Among personalized parameters, the Correction Factor is used to occasionally correct hyperglycemia via the injection of an insulin dose (bolus) and its value determines the bolus size. Although well-known in common diabetes practice for chronically poorly controlled patients, the phenomenon of "hyperglycemia induces insulin resistance" on a short term basis in patients with rather well controlled diabetes is presented here. Using a new database of evidence, we show that the insulin sensitivity factor, depends on the current level of glycaemia. This opens the door to refining dosing rules for patients and insulin delivery devices in artificial pancreas systems.

This paper presents the first autoregressive with exogenous input (ARX) model using energy expenditure, carbohydrates on board, and insulin on board as input to predict interstitial glucose (IG). The proposed model may be used for predicting IG even during physical activity (PA). A population-based model, obtained from a first database composed of 14 type 1 diabetes (T1D) patients, achieved a root-mean-square error (RMSE) of 16 . 7 ± 15 . 6 mg/dL, on IG prediction (30-min ahead) at the end of a PA, on a second database (15 T1D patients). Patient-specific ARX models, obtained on the second database, improved prediction accuracy (RMSE = 7 . 8 ± 4 . 5 mg/dL), outperforming the results found in the literature.

International audience; Objective Vagus nerve stimulation (VNS) is a potential therapeutic approach in a number of clinical applications. Although VNS is commonly delivered in an open-loop approach, it is now recognized that closed-loop stimulationmay be necessary to optimize the therapy. In this paper, we propose an original generic closed-loop control system that can be readily integrated into an implantable device and allows for the adaptive modulation of multiple VNS parameters. Methods The proposed control method consists of a state transition model (STM), in which each state represents a set of VNS parameters, and a state transition algorithm that optimally selects the best STM state, minimizing the error between an observed physiological variable and a given target value. The proposed method has been integrated into a real-time adaptive VNS prototype system and has been applied here to the regulation of the instantaneous heart rate, working synchronously with cardiac cycles. A quantitative performance evaluation is performed on seven sheep by computing classical control performance indicators. A comparison with a proportional-integral (PI) controller is also performed. Results The STM controller presents a median mean square error, overshoot, and settling time, respectively, equal to 622.21 ms(2), 72.8%, and 7.5 beats. Conclusion The proposed control method yields satisfactory accuracy and time response, while presenting a number of benefits over classical PI controllers. It represents a feasible approach for multiparametric VNS control on implantable devices. Significance Closed-loop multiparametric stimulation may improve response and minimize side effects on current pathologies treated by VNS.

In this paper, we approximate the solution of fractional differential equations with delay using a new approach based on artificial neural networks. We consider fractional differential equations of variable order with the Mittag-Leffler kernel in the Liouville-Caputo sense. With this new neural network approach, an approximate solution of the fractional delay differential equation is obtained. Synaptic weights are optimized using the Levenberg-Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional delay differential equations, linear systems with delay, nonlinear systems with delay and a system of differential equations, for instance, the Newton-Leipnik oscillator. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network, different performance indices were calculated.

This paper investigates the chaos control for a class of variable-order fractional chaotic systems using robust control strategy. The variable-order fractional models of the non-autonomous biological system, the King Cobra chaotic system, the Halvorsen’s attractor and the Burke-Shaw system, have been derived using the fractional-order derivative with Mittag-Leffler in the Liouville-Caputo sense. The fractional differential equations and the control law were solved using the Adams-Bashforth-Moulton algorithm. To test the control stability efficiency, different statistical indicators were introduced. Finally, simulation results demonstrate the effectiveness of the proposed robust control.

Neural networks and fractional order calculus have shown to be powerful tools for system identification. In this paper we combine both approaches to propose a fractional order neural network (FONN) for system identification. The learning algorithm was generalized considering the Grunwald-Letnikov fractional derivative. This new black box modeling approach is validated by the identification of three different systems (two benchmark systems and a real system). Comparisons vs others approaches showed that the proposed FONN model reached better accuracy with less number of parameters.

International audience; Although the therapeutic effects of Vagus Nerve Stimulation (VNS) have been recognized in pre-clinical and pilot clinical studies, the effect of different stimulation configurations on the cardiovascular response is still an open question, especially in the case of VNS delivered synchronously with cardiac activity. In this paper, we propose a formal mathematical methodology to analyze the acute cardiac response to different VNS configurations, jointly considering the chronotropic, dromotropic and inotropic cardiac effects. A latin hypercube sampling method was chosen to design a uniform experimental plan, composed of 75 different VNS configurations, with different values for the main parameters (current amplitude, number of delivered pulses, pulse width, interpulse period and the delay between the detected cardiac event and VNS onset). These VNS configurations were applied to 6 healthy, anesthetized sheep, while acquiring the associated cardiovascular response. Unobserved VNS configurations were estimated using a Gaussian process regression (GPR) model. In order to quantitatively analyze the effect of each parameter and their combinations on the cardiac response, the Sobol sensitivity method was applied to the obtained GPR model and inter-individual sensitivity markers were estimated using a bootstrap approach. Results highlight the dominant effect of pulse current, pulse width and number of pulses, which explain respectively 49.4%, 19.7% and 6.0% of the mean global cardiovascular variability provoked by VNS. More interestingly, results also quantify the effect of the interactions between VNS parameters. In particular, the interactions between current and pulse width provoke higher cardiac effects than the changes on the number of pulses alone (between 6 and 25% of the variability). Although the sensitivity of individual VNS parameters seems similar for chronotropic, dromotropic and inotropic responses, the interacting effects of VNS parameters provoke significantly different cardiac responses, showing the feasibility of a parameter-based functional selectivity. These results are of primary importance for the optimal, subject-specific definition of VNS parameters for a given therapy and may lead to new closed-loop methods allowing for the optimal adaptation of VNS therapy through time.

International audience; Vagus nerve stimulation (VNS) is an established adjunctive therapy for pharmacologically refractory epilepsy and depression and is currently in active clinical research for other applications. In current clinical studies, VNS is delivered in an open-loop approach, where VNS parameters are defined during a manual titration phase. However, the physiological response to a given VNS configuration shows significant inter and intra-patient variability and may significantly evolve through time. VNS closed-loop approaches, allowing for the optimization of the therapy in an adaptive manner, may be necessary to improve efficacy while reducing side effects. This paper proposes a generic, closed-loop control VNS system that is able to optimize a number of VNS parameters in an adaptive fashion, in order to keep a control variable within a specified range. Although the proposed control method is completely generic, an example application using the cardiac beat to beat interval (RR) as control variable will be developed in this paper. The proposed controller is based on a state transition model (STM) that can be configured using a partially or a fully-connected architecture, different model orders and different state-transition algorithms. The controller is applied to the adaptive regulation of heart rate and evaluated on 6 sheep, for 13 different targets, using partially-connected STM with 10 states. Also, partially and fully-connected STM defined by 30 states were applied to 7 other sheep for the same 10 targets. Results illustrate the interest of the proposed fully-connected STM and the feasibility of integrating this control system into an implantable neuromodulator.