Fuzzy logic pharmacokinetic modeling: application to lithium concentration prediction

Genetic Fuzzy System Predicting Contractile Reactivity Patterns of Small Arteries

Monitoring of physiological surrogate end points in drug development generates dynamic time-domain data reflecting the state of the biological system. Conventional data analysis often reduces the information in these data by extracting specific data points, thereby discarding potentially useful information. We developed a genetic fuzzy system (GFS) algorithm that is capable of learning all information in time-domain physiological data. Data on isometric force development of isolated small arteries were used as a framework for developing and optimizing a GFS. GFS performance was improved by several strategies. Results show that optimized fuzzy systems (OFSs) predict contractile reactivity of arteries accurately. In addition, OFSs identified significant differences that were undetectable using conventional analysis in the responses of arteries between groups. We concluded that OFSs may be used in clustering or classification tasks as aids in the objective identification or prediction of dynamic physiological behavior.

Neuro-fuzzy models as an IVIVR tool and their applicability in generic drug development

The usefulness of neuro-fuzzy (NF) models as an alternative in vitro-in vivo relationship (IVIVR) tool and as a support to quality by design (QbD) in generic drug development is presented. For drugs with complicated pharmacokinetics, immediate release drugs or nasal sprays, suggested level A correlations are not capable to satisfactorily describe the IVIVR. NF systems were recognized as a reasonable method in comparison to the published approaches for development of IVIVR. Consequently, NF models were built to predict 144 pharmacokinetic (PK) parameter ratios required for demonstration of bioequivalence (BE) for 88 pivotal BE studies. Input parameters of models included dissolution data and their combinations in different media, presence of food, formulation strength, technology type, particle size, and spray pattern for nasal sprays. Ratios of PK parameters Cmax or AUC were used as output variables. The prediction performance of models resulted in the following values: 79% of models have acceptable external prediction error (PE) below 10%, 13% of models have inconclusive PE between 10 and 20%, and remaining 8% of models show inadequate PE above 20%. Average internal predictability (LE) is 0.3%, and average external predictability of all models results in 7.7%. In average, models have acceptable internal and external predictabilities with PE lower than 10% and are therefore useful for IVIVR needs during formulation development, as a support to QbD and for the prediction of BE study outcome.

Data-driven interval type-2 neural fuzzy system with high learning accuracy and improved model interpretability

Current studies of type-2 neural fuzzy systems (FSs) (NFSs) primarily focus on building a fuzzy model with high accuracy and disregard the interpretability of fuzzy rules. This paper proposes a data-driven interval type-2 (IT2) NFS with improved model interpretability (DIT2NFS-IP). The DIT2NFS-IP uses IT2 fuzzy sets in its antecedent part and intervals in its zero-order Takagi-Sugeno-Kang-type consequent part for rule form simplicity. The initial rule base is generated by a self-splitting clustering algorithm in the input-output space. The DIT2NFS-IP uses a two-phase parameter-learning algorithm to design an accurate model with improved rule interpretability. In the first phase, a new cost function that considers both accuracy and transparent fuzzy set partition is defined. The antecedent and consequent parameters are learned through gradient descent and rule-ordered recursive least squares algorithms, respectively, to achieve cost function minimization. The second phase performs a fuzzy set reduction, followed by consequent parameter learning to improve accuracy. Comparisons with different type-1 and type-2 FSs in five databased modeling and prediction problems verify the performance of the DIT2NFS-IP in both model accuracy and interpretability.

How to initiate lithium therapy: a systematic review of dose estimation and level prediction methods

BACKGROUND

Throughout the past decades, several methods have been developed to achieve therapeutic lithium blood levels as quick and safe as possible. The present study will systematically review the methods developed and studied for lithium dose estimation or level prediction at the initiation of therapy.

METHODS

A systematic computerized Medline search was performed for papers published in English, French or Dutch between 1966 and April 2012 describing or studying methods for dosing lithium or predicting the lithium level on a certain dosage. References of relevant articles were screened for additional papers.

RESULTS

Of 273 unique references retrieved, 65 met the inclusion criteria. Apart from the empirical titration method, 38 predictive methods for initiating lithium were identified. These methods can be classified into two categories: the a priori predictive methods, and the test-dose predictive methods requiring the administration of a test dose of lithium prior to starting treatment.

LIMITATIONS

The methodological strength was not taken into account for a study to be included in the review.

CONCLUSIONS

The most important distinction between the empirical titration method and the predictive methods appears to be the shorter time the latter need to achieve the targeted lithium level. The vast majority of predictive methods, however, show inconsistent or poor results or have not been replicated since their initial description. The empirical titration method, although not extensively studied, appears to be a time-honored method that can be recommended for use in daily clinical practice.

Application of fuzzy logic to predicting erythropoietic response in hemodialysis patients

OBJECTIVE

The purpose of this study was to demonstrate how fuzzy sets can be used in a pharmacodynamic model to represent the uncertainty about the classification of an end-stage renal disease patient's response to erythropoietin.

METHODS

A pharmacodynamic model was developed to predict future hemoglobin response to administered erythropoietin for a population of 186 patients with end-stage renal failure and anemia. The prediction was performed by a weighted linear combination of past hemoglobin, transferrin saturation, and erythropoietin dose. Patients were classified based on their response to administered erythropoietin into (i) all patients into 1 group (population approach), (ii) all patients into either a poor or normal responder group (subpopulation approach--traditional classification), and (iii) all patients by partial membership into the poor and normal responder groups (subpopulation approach--fuzzy classification). One half of the data set was randomly selected to estimate the model parameters, and the second half was used to test the estimated model. This randomization was repeated 100 times for both males and females.

RESULTS

Mean square error decreased significantly through the incorporation of hemoglobin response categorization from the control group (1.32 +/- 0.07), to crisp coding (1.23 +/- 0.07), to fuzzy coding (1.20 +/- 0.07) with an overall p value < 0.001.

CONCLUSION

Uncertainty in the categorization of subjects into 2 erythropoietin response groups of poor or normal response has been shown to benefit from the use of fuzzy categories, with a significant improvement in model performance.

Spline functions in convolutional modeling of verapamil bioavailability and bioequivalence. I: conceptual and numerical issues

A cubic spline function for describing the verapamil concentration profile, resulting from the verapamil absorption input to be evaluated, has been used. With this method, the knots are taken to be the data points, which has the advantage of being computationally less complex. Because of its inherently low algorhythmic errors, the spline method is less distorted and more suitable for further data analysis than others. The method has been evaluated using simulated verapamil delayed release tablet concentration data containing various degrees of random noise. The accuracy of the method was determined by how well the estimates of input rate and extent represented the true values. It was found that the accuracy of the method was of the same order of magnitude as the noise level of the data. Spline functions in convolutional modeling of verapamil formulation bioavailability and bioequivalence, as shown in the numerical simulation investigation, are very powerful additional tools for assessing the quality of new verapamil formulations in order to ensure that they are of the same quality as already registered formulations of the drug. The development of such models provides the possibility to avoid additional or larger bioequivalence and/or clinical trials and to thus help shorten the investigation time and registration period.

Fuzzy logic in medicine and bioinformatics

The purpose of this paper is to present a general view of the current applications of fuzzy logic in medicine and bioinformatics. We particularly review the medical literature using fuzzy logic. We then recall the geometrical interpretation of fuzzy sets as points in a fuzzy hypercube and present two concrete illustrations in medicine (drug addictions) and in bioinformatics (comparison of genomes).

New Mathematical Methods in Pharmacokinetic Modeling

In recent years, several new methods for the mathematical modeling have gradually emerged in pharmacokinetics, and the development of pharmacokinetic models based on these methods has become one of the most rapidly growing and exciting application-oriented sub-disciplines of the mathematical modeling. The goals of our MiniReview are twofold: i) to briefly outline fundamental ideas of some new modeling methods that have not been widely utilized in pharmacokinetics as yet, i.e. the methods based on the following concepts: linear time-invariant dynamic system, artificial-neural-network, fuzzy-logic, and fractal; ii) to arouse the interest of pharmacological, toxicological, and pharmaceutical scientists in the given methods, by sketching some application examples which indicate the good performance and perspective of these methods in solving pharmacokinetic problems.

Fuzzy simulation of pharmacokinetic models: case study of whole body physiologically based model of diazepam

The aim of the present study is to develop and implement a methodology that accounts for parameter variability and uncertainty in the presence of qualitative and semi-quantitative information (fuzzy simulations) as well as when some parameters are better quantitatively defined than others (fuzzy-probabilistic approach). The fuzzy simulations method consists of (i) representing parameter uncertainty and variability by fuzzy numbers and (ii) simulating predictions by solving the pharmacokinetic model. The fuzzy-probabilistic approach includes an additional transformation between fuzzy numbers and probability density functions. To illustrate the proposed method a diazepam WBPBPK model was used where the information for hepatic intrinsic clearance determined by in vitro-in vivo scaling was semi-quantitative. The predicted concentration time profiles were compared with those resulting from a Monte Carlo simulation. Fuzzy simulations can be used as an alternative to Monte Carlo simulation.

Fuzzy pharmacology: theory and applications

Fuzzy pharmacology is a term coined to represent the application of fuzzy logic and fuzzy set theory to pharmacological problems. Fuzzy logic is the science of reasoning, thinking and inference that recognizes and uses the real world phenomenon that everything is a matter of degree. It is an extension of binary logic that is able to deal with complex systems because it does not require crisp definitions and distinctions for the system components. In pharmacology, fuzzy modeling has been used for the mechanical control of drug delivery in surgical settings, and work has begun evaluating its use in other pharmacokinetic and pharmacodynamic applications. Fuzzy pharmacology is an emerging field that, based on these initial explorations, warrants further investigation.

The control of blood glucose in the critical diabetic patient: a neuro-fuzzy method

Conventional algorithms for regulating insulin infusion rates in those critical diabetic patients submitted to parenteral glucose and insulin infusions do not allow to approach near normal blood glucose (BG) levels since traditional control systems are not fully effective in complex nonlinear systems as BG control is. Thus, we applied fuzzy logic principles and neural network techniques to modify intravenous insulin administration rates during glucose infusion. Forty critically ill, fasted diabetic subjects submitted to glucose and potassium infusion entered the study. They were randomly assigned to two treatment regimes: in group A, insulin infusion rates were adjusted, every 4 h at any step between -1.5 and +1.5 U/h, according to a neuro-fuzzy nomogram; in control group B, insulin infusion rates were modified according to a conventional algorithm. In group A, BG was lowered below 10 mmol/l faster than in group B (8.2+/-0.7 vs. 13+/-1.8 h, P<.02). Mean BG was 7.8+/-0.2 in group A and 10.6+/-0.3 mmol/l in group B (P<.00001). BG values below 4.4 mmol/l were: A=5.8% and B=10.2%. BG values lower than 2.5 mmol/l had never been observed. In conclusion, the neuro-fuzzy control system is effective in improving the BG control in critical diabetic patients without increasing either the number of BG determinations or the risk of hypoglycemia.

Incorporating qualitative knowledge in enzyme kinetic models using fuzzy logic

Modeling of metabolic pathway dynamics requires detailed kinetic equations at the enzyme level. In particular, the kinetic equations must account for metabolite effectors that contribute significantly to the pathway regulation in vivo. Unfortunately, most kinetic rate laws available in the literature do not consider all the effectors simultaneously, and much kinetic information exists in a qualitative or semiquantitative form. In this article, we present a strategy to incorporate such information into the kinetic equation. This strategy uses fuzzy logic-based factors to modify algebraic rate laws that account for partial kinetic characteristics. The parameters introduced by the fuzzy factors are then optimized by use of a hybrid of simplex and genetic algorithms. The resulting model provides a flexible form that can simulate various kinetic behaviors. Such kinetic models are suitable for pathway modeling without complete enzyme mechanisms. Three enzymes in Escherichia coli central metabolism are used as examples: phosphoenolpyruvate carboxylase; phosphoenolpyruvate carboxykinase; and pyruvate kinase I. Results show that, with fuzzy logic-augmented models, the kinetic data can be much better described. In particular, complex behavior, such as allosteric inhibition, can be captured using fuzzy rules. The resulting models, even though they do not provide additional physical meaning in enzyme mechanisms, allow the model to incorporate semiquantitative information in metabolic pathway models.

Using fuzzy logic to predict response to citalopram in alcohol dependence

INTRODUCTION

The prediction of patient response to new pharmacotherapies for alcohol dependence has usually not been successful with standard statistical techniques. We hypothesized that fuzzy logic, a qualitative computational approach, could predict response to 40 mg/day citalopram and 40 mg/day citalopram with a brief psychosocial intervention in alcohol-dependent patients.

METHODS

Two data sets were formed with patients from our studies who received 40 mg/day citalopram alone (n = 34) or 40 mg/day citalopram and a brief psychosocial intervention (n = 28). The output variable, "response," was the percentage decrease in alcohol intake from baseline. Input variables included age, gender, baseline alcohol intake, and levels of anxiety, depression, alcohol dependence, and alcohol-related problems.

RESULTS

A fuzzy rulebase was created from the data of 26 randomly chosen patients who received 40 mg/day citalopram and was used to predict the responses of the remaining eight patients. Eight rules related response with depression, anxiety, alcohol dependence, alcohol-related problems, age, and baseline alcohol intake. The average magnitude of the error in the predictions (RMSE) was 2.6 with a bias (ME) of 0.6. Predicted and actual response correlated (r = 0.99; p < 0.001). A fuzzy rulebase was created from the data of 28 randomly chosen patients who received 40 mg/day citalopram and a brief psychosocial intervention and was used to predict the responses of the remaining five patients. Six rules related response with age, anxiety, depression, alcohol dependence, and baseline alcohol intake with good predictive performance (RMSE = 6.4; ME = -1.5; r = 0.96; p < 0.01).

CONCLUSIONS

This study indicates that fuzzy logic modeling can predict response to pharmacotherapies for alcohol dependence.