Regulation Of Blood Glucose Concentration Research Articles

Observer‐based controller design for blood glucose regulation for type 1 diabetic patients with disturbance estimation: A backstepping approach

AbstractIn this paper, an observer‐based nonlinear controller is proposed to regulate blood glucose concentration (BGC) in type 1 diabetes mellitus (T1DM). The considered virtual patient model is the extended Bergmann minimal model, which is augmented by a meal disturbance and adapted to represent the insulin–glucose homeostasis of T1DM. The backstepping (BS) technique is used to design a closed‐loop feedback controller. The proposed controller does not need to measure insulin, plasma concentrations, and external disturbances while improving control performance and robustness against uncertainty. Insulin concentrations and plasma levels are estimated using state observers and disturbance using a disturbance estimator. These estimations are used as feedback to the controller. The asymptotic stability of the observer‐based controller is proved using the Lyapunov theorem. Furthermore, it is proven that the system is bounded input–bounded output (BIBO) stable in the presence of uncertainties caused by uncertain parameters and external disturbances. For real situations, we consider only the BGC available for measurement, and in addition, inter‐ and intra‐patient variability of system parameters is considered. The results confirm that the proposed controller can asymptotically regulate BGC through appropriate injection of insulin under meal disturbance and of variations in system parameters.

Control of Fractional Order Bergman’s Glucose-Insulin Minimal Model

Type 1 diabetes (TID) is a chronic disease which occurs by the destruction of beta cell, insulin producing hormone, in pancreas. Exogenous infusion of insulin, subcutaneously or via insulin infusion pump, is required for the regulation of blood glucose concentration in diabetic patients. In the paper is presented a comparisons among, proportional integral (PI), fractional-order proportional integral (FO-PI), sliding mode control (SMC) and fractional-order sliding mode control (FO-SMC) controllers, for the regulation of the blood glucose level utilizing the fractional-order Bergman’s minimal model. Genetic algorithms are applied to optimized the listed controllers. In analyzing the performances of the proposed controllers, meal effect is considered as an external disturbance.

Leptin is a key regulator of glucose homeostasis in obesity

Approximately 9 out of 10 people with type-2 diabetes are overweight. Leptin is a hormone secreted from white fat cells that exerts control over both food intake and energy expenditure. We described the central mechanisms underlying the hypertensive effects of hyperleptinemia in obesity. Work presented here used continuous radiotelemetric glucose monitoring in mice in combination with multiple gold standard techniques in order to determine the effects of dorsomedial hypothalamic (DMH) leptin signalling on peripheral glucose control. A leptin receptor (LepR) antagonist administered directly into the brain impaired DIO mouse glucose tolerance demonstrating that leptin retains the ability to regulate blood glucose concentration in obesity. Knockdown of DMH LepR function using short hairpin adeno-associated virus (AAV) RNA significantly reduced brown adipose tissue (BAT) thermogenesis by -0.8 ± 0.1°C and increased basal blood glucose (14.3 ± 0.6mmol/l to 9.4 ± 0.5mmol/l) and impaired glucose tolerance. Conversely, chemogenic activation of LepR-expressing DMH neurons significantly elevated BAT thermogenesis (1.5 ± 0.2 °C increase). This increased BAT temperature was immediately followed by a decrease in plasma blood glucose concentration (7.6 ± 0.5 mmol/l to 5.8 ± 0.5 mmol/l). Work presented here demonstrates that increasing the activity of LepR expressing neurons in the DMH can improve glucose tolerance in obesity though an elevation of BAT metabolic activity. This work was supported by the National Heart Foundation of Australia (SES), The National Health and Medical Research Council of Australia (SES and MAC). This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Prior-knowledge-embedded model predictive control for blood glucose regulation: Towards efficient and safe artificial pancreas

Objective:The artificial pancreas (AP) system based on model predictive control (MPC) has the potential to provide effective and reliable regulation of blood glucose concentration (BGC) for people with type 1 diabetes by utilizing glucose prediction models and appropriate safety constraints. Methods:In this work, a MPC strategy with novel model and safety constraints is proposed for BGC regularization. A prior-knowledge-embedded glucose prediction model based on kernel-regularized latent variables (LV) regression method is developed where the prediction power of the model is improved by integrating the prior knowledge of glycemic dynamics and balancing model complexity and flexibility by tuning the hyper-parameters of the kernel. Based on the prior-knowledge-embedded model, MPC strategy is formulated and BGC constraints that are not dependent on the announcement of meals and physical activity are proposed and incorporated into the MPC to reduce the risk of hypoglycemia. The benefits of the proposed model and MPC approach were evaluated through in-silico studies. Results:The proposed model achieves comparable or improved prediction accuracy with a root mean squared error of 14.08 mg/dL, 18.47 mg/dL, and 21.23 mg/dL for 30-min, 60-min, and 120-min-ahead prediction, respectively. And simulation results showed significant improvement in the time in the safe range (70–180 mg/dL) from 58.04% to 71.27% and from 78.81% to 82.31% without causing hypoglycemia. Conclusions:The proposed MPC strategy can provide safe and effective regulation of BGC without requiring manual announcements of meals and physical activity. Significance:This work is a step forward towards a fully-automated AP system.

How dietary amino acids and high protein diets influence insulin secretion.

Glucose homeostasis is the maintenance and regulation of blood glucose concentration within a tight physiological range, essential for the functioning of most tissues and organs. This is primarily achieved by pancreatic secretion of insulin and glucagon. Deficient pancreatic endocrine function, coupled with or without peripheral insulin resistance leads to prolonged hyperglycemia with chronic impairment of glucose homeostasis, most commonly seen in diabetes mellitus. High protein diets (HPDs) are thought to modulate glucose homeostasis through various metabolic pathways. Insulin secretion can be directly modulated by the amino acid products of protein digestion, which activate nutrient receptors and nutrient transporters expressed by the endocrine pancreas. Insulin secretion can also be modulated indirectly, through incretin release from enteroendocrine cells, and via vagal neuronal pathways. Additionally, glucose homeostasis can be promoted by the satiating effects of anorectic hormones released following HPD consumption. This review summarizes the insulinotropic mechanisms by which amino acids and HPDs may influence glucose homeostasis, with a particular focus on their applicability in the management of Type 2 diabetes mellitus.

Silica-Based Nanomaterials for Diabetes Mellitus Treatment.

Diabetes mellitus, a chronic metabolic disease with an alarming global prevalence, is associated with several serious health threats, including cardiovascular diseases. Current diabetes treatments have several limitations and disadvantages, creating the need for new effective formulations to combat this disease and its associated complications. This motivated the development of therapeutic strategies to overcome some of these limitations, such as low therapeutic drug bioavailability or poor compliance of patients with current therapeutic methodologies. Taking advantage of silica nanoparticle characteristics such as tuneable particle and pore size, surface chemistry and biocompatibility, silica-based nanocarriers have been developed with the potential to treat diabetes and regulate blood glucose concentration. This review discusses the main topics in the field, such as oral administration of insulin, glucose-responsive devices and innovative administration routes.

Glycolysis Regulation to Maintain Blood Glucose Homeostasis

Carbohydrates are the major source of energy for the living cells, they are the first cellular constituents that synthesized during photosynthesis from carbon dioxide and water by green plants through absorption of sun light. To be used as source of energy, carbohydrates compounds should undergo series of enzymatic metabolic stages in the cell. Beside the energy productions, catabolism of carbohydrates provides different intermediates molecules for the synthesis of biomolecules like fatty acids, amino acids, DNA, and RNA. Among the three main examples of monosaccharide (i.e: glucose, galactose, and mannose), glucose is considered as the central molecule in carbohydrate metabolism that all the major pathways of carbohydrate metabolism relate to it. Glucose is also an essential component of cellular metabolism in maintaining carbon homeostasis. Liver has shown to play a key role in monitoring and stabilizing blood glucose levels, therefore, it can be considered as glucostate monitor. In this article, we will review the major metabolic pathways of carbohydrate metabolism, their biochemical role in cellular energy production, and latest development in the understanding in these fields. Also, we discuss about the factors that participate in regulation of blood glucose concentration. We believe understand these process is essential for control scarbohydrate-related human disorders.

13C15N: glucagon-based novel isotope dilution mass spectrometry method for measurement of glucagon metabolism in humans

BackgroundGlucagon serves as an important regulatory hormone for regulating blood glucose concentration with tight feedback control exerted by insulin and glucose. There are critical gaps in our understanding of glucagon kinetics, pancreatic α cell function and intra-islet feedback network that are disrupted in type 1 diabetes. This is important for translational research applications of evolving dual-hormone (insulin + glucagon) closed-loop artificial pancreas algorithms and their usage in type 1 diabetes. Thus, it is important to accurately measure glucagon kinetics in vivo and to develop robust models of glucose-insulin-glucagon interplay that could inform next generation of artificial pancreas algorithms.MethodsHere, we describe the administration of novel 13C15N heavy isotope-containing glucagon tracers—FF glucagon [(Phe 6 13C9,15N; Phe 22 13C9,15N)] and FFLA glucagon [(Phe 6 13C9,15N; Phe 22 13C9,15N; Leu 14 13C6,15N; Ala 19 13C3)] followed by anti-glucagon antibody-based enrichment and LC–MS/MS based-targeted assays using high-resolution mass spectrometry to determine levels of infused glucagon in plasma samples. The optimized assay results were applied for measurement of glucagon turnover in subjects with and without type 1 diabetes infused with isotopically labeled glucagon tracers.ResultsThe limit of quantitation was found to be 1.56 pg/ml using stable isotope-labeled glucagon as an internal standard. Intra and inter-assay variability was < 6% and < 16%, respectively, for FF glucagon while it was < 5% and < 23%, respectively, for FFLA glucagon. Further, we carried out a novel isotope dilution technique using glucagon tracers for studying glucagon kinetics in type 1 diabetes.ConclusionsThe methods described in this study for simultaneous detection and quantitation of glucagon tracers have clinical utility for investigating glucagon kinetics in vivo in humans.

Artificial Pancreas: Avoiding Hyperglycemia and Hypoglycemia for Type One Diabetes

The objective of this work is to automatically regulate glycemia of Type 1 Diabetes Mellitus (T1DM) avoiding both hyperglycemia and hypoglycemia risks. A positive state feedback controller was designed previously to regulate Blood Glucose Concentration (BGC) in the fasting phase maintaining the system in the positively invariant set (PIS). The drawback of this positive controller is that when tested in the postprandial phase it couldn’t avoid hyperglycemia. Therefore, in this work, the positive state feedback controller was developed to avoid both hypoglycemia and hyperglycemia maintaining the system inside the PIS. Meal disturbance is estimated by a sliding mode perturbation observer to be included in the control law. Such that meal effect is canceled early enough preventing glycemia from raising to hyperglycemia, but the positivity of the new controller isn’t guaranteed. Therefore, a hybrid controller is designed to switch to the previous positive controller whenever the new controller has a negative action. A positive control is essential in this problem since the control input (insulin) can only be infused and it cannot be taken back from the bloodstream in case of any overdoses. The hybrid positive controller is tested in silico on five virtual T1DM patients. The results shown that the average percentage of time for glycemia over 180mg/dl (3.6%), normal range (80-120mg/dl) (78.2%), and below (80mg/dl) (0%) from overall simulation time. In conclusion, the hybrid positive control law succeeded to maintain the system inside the PIS avoiding hypoglycemia and preventing hyperglycemia keeping BGC in normal range rejecting meal disturbance.

Acetate wheat starch improving blood glucose response and bilan lipid on obesity dyslipidemia mice

Resistant starch is particularly concerned with beneficial effects in regulating blood glucose concentration and lipid metabolism, reducing the risk of diabetes and cardiovascular diseases. This study aimed to validate the effects of wheat starch acetate containing 32.1% resistant starch on postprandial blood glucose response and lipid profile on obesity, dyslipidemia Swiss mice induced by a high-fat diet. The result showed that there was a restriction on postprandial hyperglycemia and remained stable for 2 hours after meal efficiently comparing with the control group fed natural wheat starch. Simultaneously, when maintaining the dose of 5g/kg once or twice a day for 8 weeks, wheat starch acetate to be able to reduce body weight and blood glucose, triglyceride, cholesterol levels compared to the control group (p<0.05).

The Regulatory Effect of D-Alloxan on Glucose Metabolism and Lipid Metabolism in Diabetic Mice

To investigate the regulatory effect of d-alloxan on glucose metabolism and lipid metabolism in diabetic mice. Twenty five mice were divided into control group, glucose group, fructose group, d-alloxan group and cellulose group. The results showed that the blood glucose of mice in each group reached the peak at 90 min and the blood glucose concentration of d-alloxan group was significantly lower than that of other groups (p<0.05). The blood glucose concentration of fructose group was significantly higher than that of other groups (p<0.05). The blood glucose concentration before and after meal in d-alloxan group was significantly lower than that in other groups (p<0.05), the liver glycogen concentration before and after meal was significantly higher than that in other groups (p<0.05), the insulin level was higher than that in other groups, but the difference was not significant (p>0.05), the muscle glycogen concentration before and after meal was not significant (p>0.05). The results showed that the triglyceride concentration of d-alloxan group was significantly lower than that of other groups (p<0.05). While it was not significantly lower than that of control group (p>0.05) and there was no significant difference in total cholesterol level between groups (p>0.05). The free fatty acid concentration in glucose group, fructose group and d-alloxan group was lower than that in control group and cellulose group (p<0.05). Compared with the control group, the low density lipoprotein concentration of the other four groups was significantly lower (p<0.05) and the low density lipoprotein concentration of the d-alloxan group was significantly lower than that of the other groups (p<0.05) and there was no significant difference between them (p>0.05). The results showed that the content of succinate dehydrogenase in the blood and tissues of d-alloxan group was significantly higher than that of other groups (p<0.05) and the level of hepatic lipase in d-alloxan group was higher than that of other groups, but there was no significant difference (p>0.05). Alloxan can effectively regulate blood glucose concentration, inhibit postprandial blood glucose rise, improve insulin level and liver glycogen level, but has no significant effect on muscle glycogen. It can be used as an ideal substitute of sucrose once the disorder of lipid metabolism is improved, the ability of fat metabolism is increased and antioxidation function is improved.

REGULAÇÃO HORMONAL NO METABOLISMO ENERGÉTICO DE NÃO RUMINANTES EM ESTADO DE JEJUM

Objetivou-se com está revisão ressaltar o comportamento hormonal (insulina, glucagon, grelina, leptina, T3, T4, cortisol, adrenalina IGF e GH) atuantes no metabolismo energético de animais não ruminantes sobre o estado de jejum. Os processos metabólicos são regulados pela disponibilidade de substrato, por mecanismos neuroendócrinos. Para entender as vias metabólicas e sua regulação hormonal sobre os diferentes tecidos, faz-se necessário deter-se ao metabolismo especializado sobre os vários órgãos e tecidos que integram o metabolismo energético em todo o organismo do animal. Assim espera-se elucidar o amplo alcance dos hormônios de mobilização de energia e os mecanismos hormonais presente em cada tecido, como também descrever a inter-relação entre a insulina, o glucagon e a adrenalina na coordenação do metabolismo energético do músculo, fígado e tecido adiposo, pois cada tecido tem características metabólicas própria, de um modo geral, a concentração dos nutrientes no sangue é controlada pelo fígado, que por sua vez, torna-se o órgão central da manutenção da homeostasia dos principais nutrientes. O aporte energético no organismo durante o período de jejum se dá pela degradação de glicogênio, a proteólise muscular e lipólise que vão desempenhar papéis fisiológicos específicos para que as vias metabólicas tenham características próprias, sendo a liberação dos hormônios regulada por uma hierarquia de sinais neuronais e hormonais. A insulina, o glucagon e outros hormônios relacionados regulam as concentrações de glicose no sangue e atuam sobre o movimento de glicose, aminoácidos e, possivelmente, ácidos graxos de cadeia curta entre o fígado e os tecidos periféricos. O hormônio do crescimento pode alterar a sensibilidade dos tecidos à insulina. Na ausência de insulina, pode ocorrer a proteólise e lipólise, proporcionando substratos para a gliconeogênese e consequentemente, a produção de energia em estado de jejum.&#x0D;

Sliding-mode-based controllers for automation of blood glucose concentration for type 1 diabetes.

Destruction of β‐cells in pancreas causes deficiency in insulin production that leads to diabetes in the human body. To cope with this problem, insulin is either taken orally during the day or injected into the patient's body using artificial pancreas (AP) during sleeping hours. Some mathematical models indicate that AP uses control algorithms to regulate blood glucose concentration (BGC). The extended Bergman minimal model (EBMM) incorporates, as a state variable, the disturbance in insulin level during medication due to either meal intake or burning sugar by engaging in physical exercise. In this research work, EBMM and proposed finite time robust controllers are used, including the sliding mode controller (SMC), backstepping SMC (BSMC) and supertwisting SMC (second‐order SMC or SOSMC) for automatic stabilisation of BGC in type 1 diabetic patients. The proposed SOSMC diminishes the chattering phenomenon which appears in the conventional SMC. The proposed BSMC is a recursive technique which becomes robust by the addition of the SMC. Lyapunov theory has been used to prove the asymptotic stability of the proposed controllers. Simulations have been carried out in MATLAB/Simulink for the comparative study of the proposed controllers under varying data of six different type 1 diabetic patients available in the literature.

XPR1 Mediates the Pancreatic β-Cell Phosphate Flush.

Glucose-stimulated insulin secretion is the hallmark of the pancreatic β-cell, a critical player in the regulation of blood glucose concentration. In 1974, the remarkable observation was made that an efflux of intracellular inorganic phosphate (Pi) accompanied the events of stimulated insulin secretion. The mechanism behind this “phosphate flush,” its association with insulin secretion, and its regulation have since then remained a mystery. We recapitulated the phosphate flush in the MIN6m9 β-cell line and pseudoislets. We demonstrated that knockdown of XPR1, a phosphate transporter present in MIN6m9 cells and pancreatic islets, prevented this flush. Concomitantly, XPR1 silencing led to intracellular Pi accumulation and a potential impact on Ca2+ signaling. XPR1 knockdown slightly blunted first-phase glucose-stimulated insulin secretion in MIN6m9 cells, but had no significant impact on pseudoislet secretion. In keeping with other cell types, basal Pi efflux was stimulated by inositol pyrophosphates, and basal intracellular Pi accumulated following knockdown of inositol hexakisphosphate kinases. However, the glucose-driven phosphate flush occurred despite inositol pyrophosphate depletion. Finally, while it is unlikely that XPR1 directly affects exocytosis, it may protect Ca2+ signaling. Thus, we have revealed XPR1 as the missing mediator of the phosphate flush, shedding light on a 45-year-old mystery.

Designing a bioelectronic treatment for Type 1 diabetes: targeted parasympathetic modulation of insulin secretion.

The pancreas is a visceral organ with exocrine functions for digestion and endocrine functions for maintenance of blood glucose homeostasis. In pancreatic diseases such as Type 1 diabetes, islets of the endocrine pancreas become dysfunctional and normal regulation of blood glucose concentration ceases. In healthy individuals, parasympathetic signaling to islets via the vagus nerve, triggers release of insulin from pancreatic β-cells and glucagon from α-cells. Using electrical stimulation to augment parasympathetic signaling may provide a way to control pancreatic endocrine functions and ultimately control blood glucose. Historical data suggest that cervical vagus nerve stimulation recruits many visceral organ systems. Simultaneous modulation of liver and digestive function along with pancreatic function provides differential signals that work to both raise and lower blood glucose. Targeted pancreatic vagus nerve stimulation may provide a solution to minimizing off-target effects through careful electrode placement just prior to pancreatic insertion.

Localized Controlled Release of Bilirubin from β-Cyclodextrin-Conjugated ε-Polylysine To Attenuate Oxidative Stress and Inflammation in Transplanted Islets.

Islet transplantation has been considered the most promising therapeutic option with the potential to restore the physiological regulation of blood glucose concentrations in type 1 diabetes treatment. However, islets suffer from oxidative stress and nonspecific inflammation in the early stage of transplantation, which attributed to the leading cause of islet graft failure. Our previous study reported that bilirubin exerted antioxidative and anti-inflammatory effects on hypothermic preserved islets, which inspire us to utilize bilirubin to address the survival issue of grafted islets. However, the application of bilirubin for islet transplantation is limited by its poor solubility and fast clearance. In this study, we designed a supramolecular carrier (PLCD) that could improve the solubility of bilirubin and slowly release bilirubin to protect islets after cotransplantation. PLCD was synthesized by conjugating activated β-cyclodextrin (β-CD) to the side chain of ε-polylysine (PLL) and acted as a carrier to load bilirubin via host-guest interactions. The constructed bilirubin supramolecular system (PLCD-BR) significantly improved the solubility and prolonged the action time of bilirubin. In vitro results confirmed that PLCD-BR coculture substantially enhanced the resistance of islets to excessive oxidative stress and proinflammatory stimulation and maximumly maintained the islet function. In vivo, PLCD could prolong drug duration at the transplant site, and the localized released bilirubin could protect the islets from oxidative stress and suppress the production of inflammatory cytokines. Crucially, islet transplantation with PLCD-BR significantly extended the stable blood glucose time of diabetic mice and produced a faster glucose clearance compared to those cotransplanted with free bilirubin. Additionally, immunohistochemical analysis showed that PLCD-BR had superior antioxidative and anti-inflammatory abilities and beneficial effects on angiogenesis. These findings demonstrate that the PLCD-BR has great potentials to support successful islet transplantation.

Predicting Glycaemia in Type 1 Diabetes Patients: Experiments in Feature Engineering and Data Imputation.

Patients with type 1 diabetes manually regulate blood glucose concentration by adjusting insulin dosage in response to factors such as carbohydrate intake and exercise intensity. Automated near-term prediction of blood glucose concentration is essential to prevent hyper- and hypoglycaemic events in type 1 diabetes patients and to improve control of blood glucose levels by physicians and patients. The imperfect nature of patient monitoring introduces missing values into all variables that play important roles to predict blood glucose level, necessitating data imputation. In this paper, we investigated the importance of variables and explored various feature engineering methods to predict blood glucose level. Next, we extended our work by developing a new empirical imputation method and investigating the predictive accuracy achieved under different methods to impute missing data. Also, we examined the influence of past signal values on the prediction of blood glucose levels. We reported the relative performance of predictive models in different testing scenarios and different imputation methods. Finally, we found an optimal combination of data imputation methods and built an ensemble model for the reliable prediction of blood glucose levels on a 30-minute horizon.

Automated Insulin Delivery Algorithms.

IN BRIEF Automated insulin delivery (AID; also known as artificial pancreas) has improved the regulation of blood glucose concentrations, reduced the frequency of hyperglycemic and hypoglycemic episodes, and improved the quality of life of people with diabetes and their families. Three different types of algorithms-proportional-integral-derivative control, model predictive control, and fuzzy-logic knowledge-based systems-have been used in AID control systems. This article will highlight the foundations of these algorithms and discuss their strengths and limitations. Multivariable artificial pancreas and dual-hormone (insulin and glucagon) systems will be introduced.

Handling Parameter Variations during the Treatment of Type 1 Diabetes Mellitus: In Silico Results

Type 1 diabetic patients need a strict treatment to regulate blood glucose concentration in a target range. Despite the development of different control strategies, the model parameter variations, given by physiological changes, can generate an inaccurate treatment and in consequence hyperglycemia and hypoglycemia episodes. Therefore, it is necessary to use control techniques that compensate such effects and maintain the control goals. Here, the effect of parametric variations is examined by the sensitivity analysis from which the most influential parameters in glycemia dynamics are detected. Based on that, an offset-free MPC strategy for impulsive systems is given for the first time in literature and simulated for type 1 diabetes treatment. This scheme along with the impulsive zone MPC with artificial variables reestablishes the normoglycemia behavior since the parameter variations are adequately rejected. However, only parametric variations up to 50% from their nominal values are well compensated, which suggests that more robust formulations are needed to ensure a greater rejection of physiological variations.

Data-Driven Disturbance Estimation and Control With Application to Blood Glucose Regulation

A data-driven control approach for nonlinear systems is proposed, called data-driven estimation and control (D2EC), which combines a disturbance estimator and a nonlinear control algorithm. The estimator provides a signal representing the unknown disturbances affecting the plant to control. This signal is used by the control algorithm to improve its performance. A real-data study is presented, concerned with the regulation of blood glucose concentration in type 1 diabetic patients. Preliminary tests of the D2EC approach are also carried out using a diabetic patient simulator, obtained from a revised version of the well-known University of Virginia/Padova model. Both the real-data and the simulator-based studies indicate that the proposed approach has the potential to become an effective tool in the context of diabetes treatment and, more in general, in the biomedical field, where accurate first-principle models can seldom be found and relevant disturbances are present.