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Results for “nonlinear adaptive control”

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PubMed2003

Manipulating epileptiform bursting in the rat hippocampus using chaos control and adaptive techniques.

Epilepsy is a relatively common disease, afflicting 1%-2% of the population, yet many epileptic patients are not sufficiently helped by current pharmacological therapies. Recent reports have suggested that chaos control techniques may be useful for electrically manipulating epileptiform bursting behavior in vitro and could possibly lead to an alternative method for preventing seizures. We implemented chaos control of spontaneous bursting in the rat hippocampal slice using robust control techniques: stable manifold placement (SMP) and an adaptive tracking (AT) algorithm designed to overcome nonstationarity. We examined the effect of several factors, including control radius size and synaptic plasticity, on control efficacy. AT improved control efficacy over basic SMP control, but relatively frequent stimulation was still necessary and very tight control was only achieved for brief stretches. A novel technique was developed for validating period-1 orbit detection in noisy systems by forcing the system directly onto the period-1 orbit. This forcing analysis suggested that period-1 orbits were indeed present but that control would be difficult because of high noise levels and nonstationarity. Noise might actually be lower in vivo, where regulatory inputs to the hippocampus are still intact. Thus, it may still be feasible to use chaos control algorithms for preventing epileptic seizures.

Action Potentials↗

PubMedDate not supplied

[Can we use a Bayesian method to build a pharmacokinetic population in two steps?].

The aim of this study is to evaluate the use of a pharmacokinetic population model built by the two-stage method and individual parameters determined by a Bayesian estimation instead of nonlinear regression. We performed a retrospective analysis on 32 patient files (mean age: 82 years). First, we analysed prediction of amikacin serum levels for the Bayesian method (MAP) and nonlinear regression (MLS). Second, we compared pharmacokinetic parameter values for each patient with MAP and MLS methods for a one- or two-compartment model. For the one-compartment model, no difference in prediction performance was found (correlation coefficient: rMLS = 0.911, rMAP = 0.903, p > 0.05; precision: pMLS = 134.3, pMAP = 147, p > 0.05). A significant difference was observed only for systematic error (eMLS = -4.47, eMAP = -3.34, p < 0.05). For a two-compartment model, the Bayesian method was better for long-term prediction: 4-8 days (rMLS = 0.877, rMAP = 0.886, p > 0.05; eMLS = 5.26, eMAP = 0.04, p < 0.01; pMLS = 441.7, pMAP = 149, p < 0.05). The comparison of MAP and MLS estimated pharmacokinetic parameter values for a one-compartment model showed that the Bayesian method used to built a pharmacokinetic population in two stages does not influence pharmacokinetic parameter estimation (p > 0.05 for Vd, Kslope, Kel and t1/2). We conclude that we can use a Bayesian method to build a pharmacokinetic population in two steps in order to perform adaptative control of a drug-dosage regimen.

Aged↗

PubMed2004

Fast force-generation dynamics of human articulatory muscles.

To explore the mechanisms of speech articulation, which is one of the most sophisticated human motor skills controlled by the central nervous system, we investigated the force-generation dynamics of the human speech articulator muscles [orbicularis oris superior (OOS) and inferior (OOI) muscles of the lips]. Short-pulse electrical stimulation (300 micros) with approximately three or four times the sensation threshold intensity of each subject induced the muscle response. The responses of these muscles were modeled as second-order dynamics with a time delay (TD), and the model parameters [natural frequency (NF), damping ratio (DR), and TD] were identified with a nonlinear least mean squares method. The OOS (NF: 6.1 Hz, DR: 0.71, TD: 14.5 ms) and OOI (NF: 6.1 Hz, DR: 0.68, TD: 15.6 ms) showed roughly similar characteristics in eight subjects. The dynamics in the tongue (generated by combined muscles) also showed similar characteristics (NF: 6.1 Hz, DR: 0.68, TD: 17.4 ms) in two subjects. The NF was higher, and the DR was lower than results measured for arm muscles (NF: 4.25 Hz, DR: 1.05, TD: 23.8 ms for triceps long head), indicating that articulatory organs adapt for more rapid movement. In contrast, slower response dynamics was estimated when muscle force data by voluntarily contraction task were used for force-generation dynamics modeling. We discuss methodological problems in estimating muscle dynamics when different kinds of muscle contraction methods are used.

Electric Stimulation↗

PubMed1981

Resolution of estrogen binding species in hypothalamus and pituitary.

In addition to the classic Type I estrogen receptor, a second estrogen binding species has been reported in rat uterine nuclear material. We have examined nuclear material from hypothalamus and pituitary for the presence of Type II estrogen receptor by the sucrose pad/exchange assay. Extensive (0.05-40.0 nM) saturation analyses were performed on crude chromatin isolated from hypothalami and pituitaries of hyperestrogenized ovariectomized rats. Analysis of data by an adaptation of the graphical method of Rosenthal suggests that there is only a single class of estrogen binding sites in these tissues with a Kd (0.2 nM) close to that reported for Type I receptors in other systems. However, a definitive resolution of the binding component(s) was not possible due to noise in the upper regions of the saturation plot. Therefore, we pooled 7 hypothalamic and 4 pituitary saturation experiments and analyzed the data with LIGAND, a nonlinear curve fitting program. Computer generated curves indicate that the data from both target tissues are approximated most closely by a model describing a single high affinity binding species (Type I) (Kd = 0.17 - 0.38 nM) and a linear or very low affinity nonspecific binding component. Thus, we conclude that there is no evidence for the presence of a second or lower affinity estrogen binding component in hypothalamus or pituitary. The absence of this binding species in these two estrogen target tissues is consistent with the concept that Type II sites may be involved in estrogen's control of tissue hypertrophy and hyperplasia--estrogen responses not found in hypothalamus or pituitary.

Animals↗

PubMed2006

Decreased baroreflex sensitivity in acute schizophrenia.

Decreased vagal activity has been described in acute schizophrenia and might be associated with altered cardiovascular regulation and increased cardiac mortality. The aim of this study was to assess baroreflex sensitivity in the context of psychopathology. Twenty-one acute, psychotic, unmedicated patients with a diagnosis of paranoid schizophrenia were investigated after admission to the hospital. Results were compared with 21 healthy volunteers matched with respect to age and sex. Cardiovascular parameters obtained included measures for heart rate variability, baroreflex sensitivity, as well as cardiac output, left ventricular work index, and total peripheral resistance. All parameters investigated were analyzed using linear and novel nonlinear techniques. Positive and negative symptoms were assessed to estimate the impact of psychopathology on autonomic parameters. Subjects with acute schizophrenia showed reduction of baroreflex sensitivity accompanied by tachycardia and greatly increased left ventricular work index. Nonlinear parameters of baroreflex sensitivity correlated with positive symptoms. For heart rate variability, mainly parameters indicating parasympathetic modulation were decreased. Vascular pathology could be excluded as a confounding factor. These results reflect a dysfunctional cardiovascular regulation in acute schizophrenic patients at rest. The changes are similar to adaptational regulatory processes following stressful mental or physical tasks in healthy subjects. This study suggests that hyperarousal in acute schizophrenia is accompanied by decreased efferent vagal activity, thus increasing the risk for cardiovascular mortality. Future studies are warranted to examine the role of the sympathetic system and possible autonomic differences in hyperarousal induced by anxiety and/or external stressful events.

Adult↗

PubMed2005

Efferent-mediated fluctuations in vestibular nerve discharge: a novel, positive-feedback mechanism of efferent control.

We compared the background discharge of vestibular nerve afferents in barbiturate-anesthetized and unanesthetized, decerebrate chinchillas. Based on their interspike-interval statistics, units were categorized as regular, intermediate, or irregular. Background discharge rates were higher in irregular units from decerebrates compared to anesthetized preparations; no such difference was observed for regular or intermediate units. Large fluctuations in discharge rate were confined to intermediate and irregular units in decerebrates, but were not seen at all in anesthetized animals. The most prominent examples of fluctuations consisted of oscillations with periods exceeding 500 s and peak-to-peak amplitudes as large as 300 spikes/s. Several observations show that the fluctuations are mediated by the efferent vestibular system (EVS): (1) they are abolished when the vestibular nerve is cut proximal to the recording electrode; (2) their amplitude is correlated with the size of efferent-mediated rotational responses in individual units; and (3) they occur even when vital signs are stable. Previous studies had provided evidence that the EVS involves positive feedback: vestibular nerve afferents and EVS neurons excite one another. To study how oscillations could be produced, we developed a nonlinear model of positive feedback in which afferent feed-forward discharge was nonlinearly related to its inputs from hair cells and the EVS, while these inputs declined (adapted) as discharge was prolonged. Provided that the gain of the efferent feedback loop was sufficiently large, the model showed oscillations similar to those observed experimentally. Although large fluctuations in afferent discharge are unlikely to occur under physiological circumstances, positive feedback may be a normal feature that can amplify the influence of the EVS.

Animals↗

PubMed1996

A low-dimensional, time-resolved and adapting model neuron.

A low-dimensional, time-resolved and adapting model neuron is formulated and evaluated. The model is an extension of the integrate-and-fire type of model with respect to adaptation and of a recent adapting firing-rate model with respect to time-resolution. It is obtained from detailed conductance-based models by a separation of fast and slow ionic processes of action potential generation. The model explicitly includes firing-rate regulation via the slow afterhyperpolarization phase of action potentials, which is controlled by calcium-sensitive potassium channels. It is demonstrated that the model closely reproduces the firing pattern and excitability behaviour of a detailed multicompartment conductance-based model of a neocortical pyramidal cell. The inclusion of adaptation in a model neuron is important for its capability to generate complex dynamics of networks of interconnected neurons. The time-resolution is required for studies of systems in which the temporal aspects of neural coding are important. The simplicity of the model facilitates analytical studies, insight into neurocomputational mechanisms and simulations of large-scale systems. The capability to generate complex network computations may also make the model useful in practical applications of artificial neural networks.

Action Potentials↗

PubMed2005

[Adaptive shifts in the activity of amino acid transport into mammary secretory cells in changed nutritional conditions].

On the basis of analysis of published data, direct (using 13C) and indirect methods of estimating the amino acid transfer into mammary secretory cells in vivo were compared and the modified indirect method was used to determine quantitatively the shifts in transport activity in lactating cows and goats in trials with amino acid deficit or excess and in investigations that used a hyperinsulemic-euglycemic clamp. The analysis suggests that inadequacy of traditional use of extraction efficiency as a measure of tissue affinity to substrate is associated with two shortcomings: 1) if the changes in mammary blood flow are more expressed compared to transport activity, the arteriovenous difference and extraction efficiency may change in opposite direction to the shifts in transport activity; 2) due to the effect of nonlinearity, in situations characterized by small ratio of blood flow: the transport activity extraction efficiency is insensitive to shifts on activity of transport. The re-analysis of published data using the modified inbdirect method indicated that the deficit of individual amino acid caused a rise in activity of their transport and the excess decreased a net transfer into cell. The insulineuglycemic clamp treatments increased the activity of amino acid transport into the mammary cell and milk protein yield. The results obtained suggest that net transmembrane transfer of amino acid into mammary secretory cell can be controlled by the cell itself according to metabolic demand.

Amino Acids↗

PubMed2004

Enhanced temporal non-linearities in human object-related occipito-temporal cortex.

To what extent does neural activation in human visual cortex follow the temporal dynamics of the optical retinal stimulus? Specifically, to what extent does stimulus evoked neural activation persist after stimulus termination? In the present study, we used functional magnetic resonance imaging (fMRI) to explore the resulting temporal non-linearities across the entire constellation of human visual areas. Gray-scale images of animals, houses and faces were presented at two different presentation rates - 1 and 4 Hz - and the fMRI signal was analyzed in retinotopic and in high order occipito-temporal visual areas. In early visual areas and the motion sensitive area MT/V5, a fourfold increase in stimulus presentation rate evoked a twofold increase in signal amplitude. However, in high order visual areas, signal amplitude increased only by 25%. A control experiment ruled out the possibility that this difference was due to signal saturation ('ceiling') effects. A likely explanation for the stronger non-linearities in occipito-temporal cortex is a persistent neuronal activation that continues well after stimulus termination in the 1 Hz condition. These persistent activations might serve as a short term (iconic) memory mechanism for preserving a trace of the stimulus even in its absence and for future integration with temporally correlated stimuli. Two alternative models of persistence (inhibitory and excitatory) are proposed to explain the data.

Adaptation, Physiological↗

PubMed2005

Adaptive chaos: mild disorder may help contain major disease.

We have qualitatively analyzed different cases of human disorders and displacement activities of animals and hypothesize that some of them are examples of low-dimensional dynamical chaos in biological organisms. We also considered a biological organism in the framework of the control system theory and found that chaotic regime in one subsystem may be compensating for the loss of chaos in another subsystem for the sake of stability of the whole system. According to the hypothesis chaotic behavior of different organs sets in a human body as an alternative to serious diseases or even death. The principle of compensation was applied to different physiological systems with chaotic regimes to explain the adaptive nature of chaos there. Implications of the mechanism of adaptive chaos for sleep diseases, e.g., enuresis, and other potentially life threatening disorders of humans, e.g., RLS, are discussed in connection with the possibility to use these ideas for improved treatment strategies. The main conclusion is that adaptive disorders with chaotic symptoms should not be aggressively treated; if adaptive disorders are over treated, the whole organism may be thrown into a more regular state, which eventually will lead to a chronic disease or even death.

Adaptation, Physiological↗

PubMed1998

Pharmacokinetics and relative bioavailability of carboxyamido-triazole with respect to food and time of administration: use of a single model for simultaneous determination of changing parameters.

Carboxyamido-triazole (CAI) is an anti-invasive, antimetastatic, antiangiogenic agent in clinical development for cancer treatment. It has been postulated that food might enhance the oral absorption of micronized CAI based on an apparent discrepancy in steady state maximum concentrations when taken without regard to meals vs. fasting. The purpose of this study was to determine if a standardized meal affects the absorption and pharmacokinetics of this agent. Twelve patients with refractory cancers and good end organ function were randomized to receive two doses of CAI (250 mg/m2) with and without a standardized high fat meal. One cohort of 6 patients received these doses at 9 AM, and the remaining 6 patients received CAI at 9 PM. Blood was obtained prior to each dose, and serially thereafter. A series of pharmacokinetic (PK) models were fit to the concentration-time data. PK parameters were ultimately calculated using a model which allows simultaneous estimation of parameters from both test doses using nonlinear least squares analysis with ADAPT II. This model estimates independent absorption rate constants and relative fraction absorbed for each condition. AUC0-t was determined using the trapezoidal method, extrapolated to infinity, and used to calculate the relative bioavailability. No significant differences in PK parameters were noted between the morning and evening cohorts. However, the relative bioavailability, as measured by AUC0-infinity, of CAI was significantly increased when administered with a high fat meal compared to fasting (138.9 vs. 52.2 micrograms * hr/ml; p = 0.0005). The magnitude of the increase in relative bioavailability of CAI taken with food could have profound implications for patients who may inadvertently take this medication shortly after eating.

Adult↗

PubMed2006

Learning from neural control.

One of the amazing successes of biological systems is their ability to "learn by doing" and so adapt to their environment. In this paper, first, a deterministic learning mechanism is presented, by which an appropriately designed adaptive neural controller is capable of learning closed-loop system dynamics during tracking control to a periodic reference orbit. Among various neural network (NN) architectures, the localized radial basis function (RBF) network is employed. A property of persistence of excitation (PE) for RBF networks is established, and a partial PE condition of closed-loop signals, i.e., the PE condition of a regression subvector constructed out of the RBFs along a periodic state trajectory, is proven to be satisfied. Accurate NN approximation for closed-loop system dynamics is achieved in a local region along the periodic state trajectory, and a learning ability is implemented during a closed-loop feedback control process. Second, based on the deterministic learning mechanism, a neural learning control scheme is proposed which can effectively recall and reuse the learned knowledge to achieve closed-loop stability and improved control performance. The significance of this paper is that the presented deterministic learning mechanism and the neural learning control scheme provide elementary components toward the development of a biologically-plausible learning and control methodology. Simulation studies are included to demonstrate the effectiveness of the approach.

Algorithms↗

PubMed2005

Improving the estimation of change from baseline in a continuous outcome measure in the clinical trial setting.

In many clinical trials, the primary focus is whether treatment groups differ with respect to the change from baseline to end of therapy in a continuous response variable. Randomized clinical trials often use a repeated measures design in which subjects are followed-up at fixed times throughout the study. With this design, testing for differences between treatment groups with respect to the average change from baseline to end of therapy in the response variable is equivalent to testing for differences between the rates of change in the response variable, assuming the rates of change in each treatment group are linear. This analysis can be performed quite easily using methods such as generalized estimating equations (GEE). However, if the rate of change in the response cannot be assumed linear, the average change from baseline is many times calculated using simply differences between baseline and final measurements and additional data points are not included in the analysis. Instead, we propose using all available data in a repeated measures model that is based on the nonlinear treatment response pattern to estimate the average change from baseline to end of therapy in each treatment group. GEE with robust variance estimation is used for obtaining these model-based estimates of the treatment effect and a simple test for appropriateness of the model is presented. The GEE model presented, in conjunction with the test for appropriateness of the model, form the basis for an adaptive analysis approach for determining the method of estimation of the primary endpoint. This approach results in more efficient estimates of the treatment effect when the response pattern is specified correctly and minimizes the bias in the estimate when the hypothesized response pattern is misspecified. We are motivated by examples in the cystic fibrosis (CF) clinical trial setting and demonstrate the potential for this approach in reducing the sample size required for future CF clinical trials.

Computer Simulation↗

PubMed2002

Models of skeletal muscle to explain the increase in passive stiffness in desmin knockout muscle.

Absence of desmin in skeletal muscle was found to induce an increase in passive stiffness. The present study aimed at developing rheological models of passive muscle to explain this stiffening. Models were elaborated by using experimental data depicting muscle viscoelastic behaviour. The experimental protocol included stepwise extension tests applied on control and desmin knockout soleus muscles from mice. Linear and non-linear models were composed of elastic and viscous elements. They were constructed with the aim at taking the presence or absence of desmin into account by simulating desmin as an elastic element. Furthermore, associated adaptation of connective tissues in absence of desmin was modelled as an additional elastic element. Differences in passive behaviour induced by absence of desmin were predicted by using a linear model and a non-linear one. The non-linear model was selected because: (1) it is able to predict experimental viscoelastic kinetics accounting for the increase in passive stiffness in muscles lacking desmin, (2) its design is consistent with morphological data, and (3) stiffness characteristics of its elements are in accordance with the literature. Finally, this modelling approach demonstrates that both absence of desmin and adaptation of connective tissue are required to explain the increase in passive stiffness in desmin knockout muscles.

Animals↗

PubMed2006

Modifying the baricity of local anesthetics for spinal anesthesia by temperature adjustment: model calculations.

BACKGROUND: Although local anesthetics (LAs) are hyperbaric at room temperature, density drops within minutes after administration into the subarachnoid space. LAs become hypobaric and therefore may cranially ascend during spinal anesthesia in an uncontrolled manner. The authors hypothesized that temperature and density of LA solutions have a nonlinear relation that may be described by a polynomial equation, and that conversion of this equation may provide the temperature at which individual LAs are isobaric. METHODS: Density of cerebrospinal fluid was measured using a vibrating tube densitometer. Temperature-dependent density data were obtained from all LAs commonly used for spinal anesthesia, at least in triplicate at 5 degrees, 20 degrees, 30 degrees, and 37 degrees C. The hypothesis was tested by fitting the obtained data into polynomial mathematical models allowing calculations of substance-specific isobaric temperatures. RESULTS: Cerebrospinal fluid at 37 degrees C had a density of 1.000646 +/- 0.000086 g/ml. Three groups of local anesthetics with similar temperature (T, degrees C)-dependent density (rho) characteristics were identified: articaine and mepivacaine, rho1(T) = 1.008-5.36 E-06 T2 (heavy LAs, isobaric at body temperature); L-bupivacaine, rho2(T) = 1.007-5.46 E-06 T2 (intermediate LA, less hypobaric than saline); bupivacaine, ropivacaine, prilocaine, and lidocaine, rho3(T) = 1.0063-5.0 E-06 T (light LAs, more hypobaric than saline). Isobaric temperatures (degrees C) were as follows: 5 mg/ml bupivacaine, 35.1; 5 mg/ml L-bupivacaine, 37.0; 5 mg/ml ropivacaine, 35.1; 20 mg/ml articaine, 39.4. CONCLUSION: Sophisticated measurements and mathematic models now allow calculation of the ideal injection temperature of LAs and, thus, even better control of LA distribution within the cerebrospinal fluid. The given formulae allow the adaptation on subpopulations with varying cerebrospinal fluid density.

Air Pressure↗

PubMed1999

Statistical physics and physiology: monofractal and multifractal approaches.

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.

Biophysical Phenomena↗

PubMed2002

The K-Cl cotransporter in the lobster stretch receptor neurone--a kinetic analysis.

Experiments were performed to define quantitatively the substrate (K(+) and Cl(-)) dependence of the transport function (production of equally large and oppositely directed K(+)and Cl(-) flows/currents) of an earlier (Theander et al., 1999) identified electroneutral K-Cl cotransporter in the slowly adapting stretch receptor neurone of the European lobster. The experiments were based on microelectrode techniques. This allowed us to perform steady-state measurements of the so-called "instantaneous" current-voltage relationships (around a holding voltage of -65 mV after a blockage of the cell's action potential and hyperpolarization-activated currents) and intracellular ion concentrations at various settings of the extracellular K(+) and Cl(-) concentrations. From the results, we could then define steady-state values of all of the cell's non-KCl cotransporter K(+) and Cl(-) currents. Finally, the negative sums of the inferred non-KCl cotransporter K(+) and Cl(-) currents could be taken as equivalents of the K-Cl cotransporter's K(+) and Cl(-) currents for the reason that, in steady state, all membrane currents add up to zero. For the cotransporter currents, thus inferred for a range from 2.5/410.5 to 40.0/448.0 mM external K(+)/Cl(-), we found that their absolute values increased in a nonlinear fashion from about 5 nA cell(-1) at the lowest, to about 20 nA cell(-1) at the highest external K(+)/Cl(-) concentrations. Formally, this relationship could be reproduced by a Hill function-based enzyme kinetic expression simulating inward and outward transmembrane electroneutral ion transports. Following insertion of this expression into a comprehensive model of electrical membrane functions and intracellular solute and solvent control in the lobster stretch receptor neurone, the model predictions suggested that the K-Cl cotransporter does play an important role in (a) keeping intracellular Cl(-) low for a proper function of the cell's inhibitory system, and (b) enabling rapid transmembrane K(+) shifts that provide for a stabilization of the cell's membrane voltage and membrane excitability in cases of varying extracellular K(+) concentrations. The model predictions gave, however, no clear evidence that the K-Cl cotransporter is critically involved in the cell's volume regulation in conditions of varying extracellular osmolalities.

Animals↗

PubMed2005

Conversion-dependent shrinkage stress and strain in dental resins and composites.

The placement of dental composites is complicated by the contraction that accompanies polymerization of these materials. The resulting shrinkage stress that develops during cure of a bonded restoration can induce defects within the composite, the tooth or at the interface resulting in compromised clinical performance and/or esthetics. In light of the substantial efforts devoted to understanding and attempting to control shrinkage stress and strain in dental composite restoratives, this paper offers a perspective on the conversion dependent development of shrinkage and stress. The relationships between polymer property development and the physical evolution of the network structures associated with dental polymers as well as the interrelated kinetics of the photopolymerization reaction process are examined here. Some of the methods used to assess conversion in dental resins and composites are considered. In particular, newly introduced techniques that allow real time analysis of conversion by near-infrared spectroscopy to be coupled directly to simultaneous dynamic measurements of either shrinkage stress or strain are described. The results are compared with reports from the dental materials literature as well as complementary studies in other related fields of polymer science. The complex, nonlinear correlation between conversion, shrinkage and stress are highlighted. A brief review of some of the materials-based approaches designed to minimize polymerization shrinkage and stress is also provided.

Composite Resins↗