Clinical Applications of Artificial Neural Networks in Pharmacokinetic Modeling

Clinical Applications of Artificial Neural Networks in Pharmacokinetic Modeling

CHAPTER 20 Clinical Applications of Artificial Neural Networks in Pharmacokinetic Modeling Syeda Saba Kareem1, Yashwant Pathak2 1 Pharmacy Department...

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Clinical Applications of Artificial Neural Networks in Pharmacokinetic Modeling Syeda Saba Kareem1, Yashwant Pathak2 1

Pharmacy Department, St. Joseph’s Hospital, Tampa, FL, USA; 2USF College of Pharmacy, University of South Florida, Tampa, FL, USA

1. INTRODUCTION Artificial neural networks (ANNs) can be utilized in multiphase pharmaceutical development from drug structure to functionality. The potential applications of ANNs utilize their ability to process complex variables, recognize patterns, and predict functions [1]. These applications include drug design, dosage recognition, and pharmacokinetic and pharmacodynamic modeling. ANNs are able to process and simulate various nonlinear systems with dependent and independent physiological variables [2].

2. WHAT ARE ANNs? 2.1 Introduction to ANNs ANNs are computational tools or models for making decisions, drawing conclusions, and adapting to different situations. They can generalize relationships between dependent and independent variables without fixed mathematical function [1]. ANN systems were designed to simulate the way the brain retrieves, processes, and stores information. The network is able to make decisions and draw conclusions from incomplete information and to adapt to novel situations [3]. It can be used to simulate nonlinear complex scenarios such as in pharmaceutical research [2]. The main concept of the ANN system is to simulate the biologic neurological processing unit to analyze data and learn from experiences. The brain consists of millions of interconnected neurons where an input is received and processed and an output signal is transmitted. Dendrites carry signals into the cell body, which receives and processes the information. The axon then carries the signal away from the cell body to other dendrites or target cells. All of these connections enable the brain to recognize patterns, learn, and predict outcomes [4]. The basic components of the ANN follow a similar system, which is Artificial Neural Network for Drug Design, Delivery and Disposition. Copyright © 2016 Elsevier Inc. All rights reserved.

CONTENTS 1. Introduction .. 393 2. What Are ANNs?........... 393 2.1 Introduction to ANNs................... 393

3. ANNs in Pharmacokinetic and Pharmacodynamic Modeling ....... 394 3.1 Quantitative StructureePK Relationships...... 395 3.1.1 Absorption...........395 3.1.2 Distribution .........396 3.1.3 Metabolism and Excretion .............396

3.2 PK Modeling ....... 396 3.2.1 Modeling Techniques in PK....................396 3.2.2 Applications of PK Modeling Utilizing ANN.....................397

4. Clinical Application of ANNs............. 398 4.1 Overview of Clinical Applications ........ 398 4.2 PK/PD Modeling of Repaglinide......... 398




Clinical Applications of Artificial Neural Networks in Pharmacokinetic Modeling

4.3 Control of Induced Paralysis Using Vecuronium Bromide .............. 399 4.4 Aminoglycoside Pharmacokinetics in Severely Ill Patients............... 399 4.5 Low Therapeutic Index Medications ........ 400 4.5.1 Classification of Patients with Potential Risk for Digoxin Toxicity ...400 4.5.2 Prediction of Cyclosporine Dose ....................400

4.6 Predicting Epoetin Responsiveness.. 401 4.7 Warfarin Dose Individualization . 401

5. Conclusion .... 402

characterized by its processing unit, learning rules, and connection formulas [5]. In the processing unit, a commonly applied ANN layout is when a forward-propagating network is utilized. This is where input layers receive data from an external source, which is then mapped by a neural network of hidden layers, and then an output signal is generated and transmitted via an output layer [6]. ANNs are able to learn nonlinear relationships while minimizing error between the estimated and experimental data through a process called backpropagation [2]. The method utilizes three steps of network: design, training, and usage. In the process of training, weights of the connections between processing units are adjusted until an optimal network state is achieved [2,3]. The amount of training is important because an undertrained ANN can output a large amount of error, whereas an overtrained ANN may not be flexible enough to recognize patterns in the data used [7]. ANN modeling can be supervised or unsupervised with different applications and expectations. In supervised learning, the goal is to predict target values from one or more input variables, and it relies on pairs of input and output sets [8]. Supervised learning provides an alternative to conventional response surface methodology (RSM). In unsupervised learning, inputs are provided but not with any paired outputs. This causes the system to self-organize and adapt based on the variables given. The goal is to develop pattern recognition and association. In the pharmaceutical field, RSM can be used as an alternative to principal component analysis [2]. ANNs are different from other statistical models in their ability to generalize behavior through data modeling, learning, and complex pattern recognition [1e30]. It is a dynamic tool that is able to process nonlinear data with intricate variables. This ability is imperative in complex multilayered modeling, such as in pharmaceutical studies [9,10].



Pharmacokinetic (PK) modeling relates to the prediction of concentratione time profiles of a drug in the body after drug administration. It is the study of the absorption, distribution, metabolism, and elimination (ADME) processes of the drug. There are multiple modeling and simulation techniques used to predict the way a drug responds to the body. Pharmacodynamic (PD) modeling relates to the relationship of the drug concentration to the pharmacological response. One of the ways that a response can be achieved is by binding to a receptor. Once the drug is bound to a receptor, the drug-induced activation or inhibition can lead to the observed pharmacological response. This relationship between drug concentration and positive/negative response can be further studied via simulation and modeling techniques [11,12].

3. ANNs in Pharmacokinetic and Pharmacodynamic Modeling

The relationship between pharmacokinetics and pharmacodynamics is to determine the appropriate dosing regimen of a drug to achieve the required pharmacological response in the body. The goal in utilizing PK/PD studies is to determine meaningful correlations between measurable variables such as plasma concentrations to yield the desired therapeutic response [13]. This information is useful in drug selection, development, and dosing regimens. There are multiple parametric and nonparametric methods to determine these relationships, but these existing methods do have challenges. Active drug molecules interact with complex biological processes, including endogenous ligand interactions and PK changes, yielding different forms of the drug molecule. Traditional modeling procedures require vast assumptions and knowledge of these types of underlying mechanisms. Lack of such information regarding a drug compound in preclinical studies would disrupt accurate and effective drug design [11]. The preliminary PK properties and drug effects are usually studied using in vivo and in vitro methods. Because of the many potential drug candidates, and the resource constraints to provide data for each drug, computational modeling provides an advantageous option. The increasing availability, accuracy, and processing power of computational technology, or “in silico” methods, have made it a useful tool in the drug development process [14e16]. Because of the flexible nature of ANNs, they can provide a versatile alternative as a model-independent approach to processing PK/PD data. ANNs that are used in PK/PD models can be composed of multiple layers, including the input layer, PK compartment layer, receptor layer, and pharmacological output layer [18]. ANNs can be used to generalize the association of drug concentrations with detected functional effects and interpret analytical data and process in vitro/in vivo correlations [19]. They can incorporate evidence-based and experimental data to solve problems, and they can be utilized to predict PK/PD profiles before more invasive and expensive techniques.

3.1 Quantitative StructureePK Relationships Computational testing for ADME incorporates the complexities of pharmacokinetics, including quantitative structure and activity relationship modeling. This takes into account spatial arrangement of atoms in the drug molecule and the interaction of the molecules with the receptor. This is dependent on the three-dimensional configuration and conformation of the molecule, which allows for binding and subsequent functionality. Other computational techniques account for electrostatic and steric bonding and interaction. Other structural properties that can influence ADME include hydrogen bonding, lipophilicity, permeation, and bioavailability [20e22].

3.1.1 Absorption Bioavailability can be affected by absorption of a drug and the site of administration [20]. Characteristics that can affect the rate and extent of absorption




Clinical Applications of Artificial Neural Networks in Pharmacokinetic Modeling

include chemical state, aqueous solubility, lipophilic profile, and threedimensional structure. ANN modeling has also been used in skin permeation studies because of the multivariable nature of absorption [23e25].



After the drug is absorbed, it gets distributed via the circulatory system into extravascular fluids and tissue to get to the target destination. Some drugs bind to proteins, and this can affect its distribution patterns [20]. The partitioning of drugs between tissue and blood can be defined by utilizing the partition coefficient Pt:b ¼ Ct/Cb (Ct is the concentration of drug in tissue, and Cb is the concentration of drug in blood). Mechanistic and ANN techniques can be utilized to predict tissue:blood/plasma levels. The volume of distribution (Vd) can represent the theoretical volume in which a drug is distributed. A high Vd can indicate the preference of the drug in tissue, whereas a low Vd can indicate drug mainly in the plasma. Vd can have linear and nonlinear relationships, and nonlinear predication has been done utilizing ANN models [26,27].


Metabolism and Excretion

Elimination of a drug out of the body can occur by metabolism and excretion. Metabolism is the process of chemical conversion in which the initial drug is transformed into metabolites. These metabolites can be pharmacodynamically active or inactive. Excretion is the process in which the metabolites are eliminated from the body via the renal or hepatobilary pathway. Compounds can be metabolized via reduction, oxidation, hydrolysis, or conjugation reactions. Structural differences affecting the enzymatic pathway can also affect the rate of reactions. The structureemetabolism relationship and clearance can also be analyzed utilizing ANN methodology [28e30].

3.2 3.2.1

PK Modeling Modeling Techniques in PK

PK modeling utilizes mathematical tools to represent multifaceted physiological processes, and there are different modeling techniques used. One such commonly used approach is the multilinear regression (MLR) model that utilizes mathematical regression equations. This analysis approach is based on a concept that the physiochemical properties of a molecule can be combined in a linear and additive way to estimate activity. It involves a frequentative process in which the spectrum of a substance can be deconstructed and regenerated to mathematically synthesized spectrums [2]. One of the advantages of this type of model is the direct relationship between the variable and target activity. Some disadvantages include that fact that it can be a very tedious and timeconsuming process in which a small amount of descriptor variables are used, making it difficult to construct meaningful models [16,31]. ANNs can be used as a data-modeling tool and can be trained to recognize specific pattern

3. ANNs in Pharmacokinetic and Pharmacodynamic Modeling

of constituents from the overall spectral pattern in a faster and more precise manner [32]. RSM is another technique used to predict pharmaceutical responses and is used in formulation optimization. It utilizes second-order polynomial equations to predict pharmaceutical responses for optimal product formulations. ANNs have been shown to have better predicting abilities in the development of dosage formulations while varying multiple factors [9,33]. Nonlinear mixed-effect modeling (NONMEM) is another type of program that is used in the analysis of PK and PD data. It is a nonlinear regression program that includes fixed and random parameter effects, and response variables can change with alterations in the predictor variable. ANNs have been used in population PK data analysis and have been found to be superior to NONMEM by having fewer prediction errors and average absolute errors [34e36].

3.2.2 Applications of PK Modeling Utilizing ANN ANN modeling can be used as an effective tool in quantification of various pharmaceutical preparations. One of the difficulties of using a traditional quantitative approach for formulation design includes understanding the causal relationship between different variables and pharmaceutical response [37e39]. In the classical approach, the formulation factors need to be understood and the variables are processed based on the formulation of the product desired. Composite experimental designs utilizing several factors and variables are applied to select rational model formulations. Using ANNs as an approach would vastly decrease the amount of time doing one-on-one experimentation for preparing the model formulation [2]. Response variables of the formulations are predicted quantitatively by a combination of factors, and ANNs are effective in this case because the functional dependence between inputs and outputs are not linear [40e42]. Neural networks are also useful in analyzing physical and chemical properties that are core components of PK determination [20]. There are multiple studies that have utilized ANNs in high-performance liquid chromatography optimizations for prediction of retention times [43,44]. The chromatographic behavior of solutes and components of the mobile phase were analyzed, and the predictive capacity factors of solutes obtained by ANNs were more precise than those obtained by MLR models [45,46]. ANNs can also be useful in determining the composition of unknown samples by superimposing a known spectrum over the unknown [47]. Neural networking has also been used in predicting phase behaviors of quaternary microemulsion forming systems [48]. In vitro and in vivo correlation (IVIVC) studies have also been done utilizing ANN methodology. They can be used to predict in vivo results from in vitro studies and increase efficiency when analyzing different formulations of the same product. IVIVC studies are important to avoid unnecessary bioequivalence studies that may produce negative results [19,34].




Clinical Applications of Artificial Neural Networks in Pharmacokinetic Modeling

4. 4.1

CLINICAL APPLICATION OF ANNs Overview of Clinical Applications

There are multiple studies that have been conducted that apply the concept of artificial neural networking to current clinical practices. There are many medical decisions that can be made based on this flexible tool of prediction to enhance pharmaceutical dosing and hence clinical application. The following are examples of the clinical application of ANNs in current literature. Initial results from these studies are indicating the usefulness of such programming tools to better understand the drugs’ effects on the body and the body’s response to the drug.


PK/PD Modeling of Repaglinide

Repaglinide is a unique oral insulin secretagogue agent that is used in the management of type II diabetes mellitus and can be used in combination with metformin or thiazolidinediones. A study was done to investigate the utility of ANNs in recognizing relationships among patient variables, PK parameters, and PD response to repaglinide. The methodology utilized phase II placebocontrolled trial data that included repaglinide plasma concentrations, blood glucose levels, and patient demographic information. Seventy percent of the data were partitioned into training sets whereas the remaining 30% were used as a test set. A predictive PK data modeling program using neural networking analysis concepts was developed, and covariant and independent variables including age, gender, weight, dose, and week of treatment were used. The dependent variable of repaglinide area under the curve (AUC) was used as an output factor. This model was used to assess the effect of the dose and demographic variable on the level of drug in the body. A predictive PKePD model was also developed utilizing the repaglinide AUC as a covariant, and the glucose AUC was an output or dependent variable. This would test the body’s response to the drug by the level of glucose control achieved. The predicted performance from the ANN models was tested by comparing the ANN results with naïve averaging or random generation of the data. The results showed that the PK model resulted in more precise data than the random or average comparisons. The PKePD model was much less precise, and this was attributed to a lack of sufficient training and multiple known and unknown factors, which can affect glucose levels. The PKePD model utilizing ANN techniques resulted in data that could be comparable to traditional PKePD models, signifying the complexities associated with PD models and its effects from multiple variables. However, both model sets showed good precision with minimal bias of the test sets when compared with the training sets. This study showed that PK and PKePD models can be developed utilizing artificial neural networking systems that can yield relatively fast, easy results that are consistent with traditional methods [49].

4. Clinical Application of ANNs

4.3 Control of Induced Paralysis Using Vecuronium Bromide Vecuronium is a neuromuscular blocking paralytic agent that is used to facilitate intubation and ventilation as well as to eliminate muscle stimulation during surgery. An anesthesiologist is generally able to control the level of induced paralysis by altering the amount of paralytic agent being given. Vecuronium is one such agent, with a rapid onset and metabolism in the body. Previous studies have shown the PK model of Vecuronium to be linear; however, the PD model and the overall response are more static and nonlinear. This study proposed to test an ANN-based controller to help regulate the level of induced paralysis. The ANN model allows for an ample amount of training utilizing the nondecreasing property of the patient response to directly control the infusion rate of the medication. The program utilized a patient response model that consisted of PK and PD data. The ANN controller was a multilayer model that consisted of an input later with 18 nodes, two hidden layers with 25 nodes, and an output layer with 1 node. The controller was trained with data using nominal patient response parameters, but it was able to control the level of paralysis of patients with different response characteristics. The steady-state error of the ANN model was negligible, and the mean steady-state drug infusion rate to achieve satisfactory paralysis was 1.22 mg/kg/min. This was comparable to average values reported in the literature from other methods. The training did not need to be specific to the patient because nominal patient parameters yielded adequate results. Multiple advantages were seen using this model, including adaptability to nonlinear changes and eliminating the need for multiple algorithms to detect transient or steady-state responses [50].

4.4 Aminoglycoside Pharmacokinetics in Severely Ill Patients Aminoglycosides are a category of Gram-negative antibiotics that can have significant individual variability between dose and plasma levels and requires therapeutic drug monitoring with peak and trough levels. Severely ill patients in the intensive care unit have complex PK characteristics that can make predicting plasma levels difficult. A study was done to investigate the use of ANNs to predict plasma levels using parameters related to severity of illness. Patient data that were collected included age, weight, medication dose, and multiple parameters that would assess the severity of the illness. All of these variables were used to train an ANN model that consisted of three structural layers. An input layer, a hidden layer with 10 processing elements, and an output layer with 2 processing elements for the peak and trough. MLR analysis was also done to be used as a comparator for predicting the plasma levels. The severity of the illness tends to cause more of a nonlinear relationship between the physiological measurements and plasma levels. This study showed that the predicted performance of




Clinical Applications of Artificial Neural Networks in Pharmacokinetic Modeling

using ANNs was better than using MLR methodology when analyzing plasma levels of aminoglycosides utilizing severity parameters. However, the volume of distribution and clearance of aminoglycosides were also calculated, but they were shown to have more of a linear relationship that was not adequately predicted by ANN modeling. This showed that ANNs performed better when using nonlinear parameters such as the severity of illness, but linear modeling would be more appropriate for linear systems [51].

4.5 4.5.1

Low Therapeutic Index Medications Classification of Patients with Potential Risk for Digoxin Toxicity

Digoxin is an antiarrhythmic cardiac glycoside agent that is indicated for patients with atrial fibrillation or heart failure. It has a very narrow therapeutic index, which can inadvertently lead to toxic effects when blood concentrations are above therapeutic ranges. Software programming utilizing neural networking concepts was developed to identify patients that could be at risk for getting digoxin toxicity. The model included 14 input variables, including physiological and treatment factors, as well as nine nodes in the hidden layer. The output node incorporated the upper normal limit of the digoxin range to identify patients at risk for toxicity. Patient data were incorporated into training and validation sets, and the resultant data were shown with recommendations for the specialist to alert at-risk patients [52e54]. This type of application highlights the potential for ANNs to be incorporated within clinical software to allow for efficient stratification of high-risk patients.


Prediction of Cyclosporine Dose

Cyclosporine is a calcineurin inhibitor that acts as an immunosuppressive agent primarily used in the transplant setting. It also has a narrow therapeutic index with specific ranges depending on the indication. Underdosing can lead to decreased efficacy and complications with grafts whereas overdosing can lead to toxic side effects including organ damage and infections. Cyclosporine pharmacokinetics are further complicated because of greater interpatient variables that affect absorption and metabolism. A study utilizing multiple dynamic forms of ANNs was conducted to predict dosing information for cyclosporin to target specific reference ranges. Patient data that were used to train and validate the programs included daily dose, serum creatinine, weight, and cyclosporin levels. No statistical difference was noted between the different types of ANNs; however, the study concluded that neural networks are clinically useful as a tool for therapeutic drug monitoring. Further studies with larger samples sizes need to be conducted to compare the predictive performance between the different types of ANN models [52,55].

4. Clinical Application of ANNs

4.6 Predicting Epoetin Responsiveness Erythropoietin is a glycoprotein hormone that controls the production of red blood cells, and it can be used to manage the anemia that is an inevitable complication of end-stage kidney disease. An optimal hemoglobin/hematocrit range is recommended to be maintained; however, the response to erythropoietin can have large variability depending on patient factors, iron status, dialysis efficiency, vitamin deficiency, pharmacological agents, and comorbidities. Individualizing epoetin doses becomes particularly difficult because of the increased variability. A study was done to analyze the linear and nonlinear relationships of clinical and biological variables and the response to epoetin. The methodology included collecting patient data, including age, sex, weight, hemoglobin, and epoetin dose and route. ANNs were developed, trained, and tested to process the nonlinear continuous function between patient data and epoetin dose. All study variables were analyzed separately and then combined to achieve an optimal prediction response. A comparator of a linear regression model was used that plotted epoetin dose with the hemoglobin level. A further comparator utilized a prediction by nephrologists who were following up hemoglobin levels below the target range. The sensitivity, specificity, and the positive and negative predictive values were calculated by interpreting the decision of nephrologists to increase or decrease the epoetin dose. The sensitivity of ANNs compared with a linear regression model for predicting erythropoietin doses to reach target was 78% and 44%, respectively. The sensitivity in predicting hemoglobin values below the target level comparing ANNs with nephrologist prediction was 45% and 25%, respectively. These results showed that ANNs were able to more precisely predict dose responses when compared with linear regression models and physician opinions, and they are a viable option for individualizing doses. ANNs have the advantage of tolerating missed data and errors in individual variables, and they are able to translate multivariate nonlinear relationships into continuous functions [56].

4.7 Warfarin Dose Individualization Warfarin is a vitamin K antagonist that is used as an oral anticoagulant agent in the prevention and treatment of thromboembolic disorders and embolic complications arising from atrial fibrillation or valve replacement. There is a narrow therapeutic index (international normalized ratio [INR] usually 2e3), and any change beyond this range can lead to thrombotic or bleeding events, both of which can be fatal. Individualizing doses can be challenging because of the large patient variability in dosing requirements. Multiple factors including age, gender, diet, weight, comorbidities, concurrent medications, and genetic variability can affect warfarin pharmacokinetics and pharmacodynamics. A study was done to compare individualized warfarin dosing utilizing ANN modeling and traditional warfarin dosing algorithms. Appropriate patient




Clinical Applications of Artificial Neural Networks in Pharmacokinetic Modeling

factors and data were collected and divided into derivation and validation sets. The derivation sets were used to select appropriate models because there were different ANN models utilizing various input variables. ANN models were able to provide acceptable predictions that explained 43e48% of the dose variability among patients, and traditional warfarin dosing algorithms predicted the ideal dosage in 46% of the total cohorts. The predictable performance and clinical value were shown to be comparable to traditional dosing algorithms. ANNs can provide a faster alternative to manual algorithms, and further individualized dosing can be explored [57]. Another warfarin study was done to compare predictive effects of ANNs to MLR models when individualizing dosing in patients. Data collected were assigned to be divided into training and validation sets. The output variable was the appropriate maintenance dosage of warfarin to reach the target INR levels. The results showed ideal predictive percentages of 66e68% for the ANN model and 45e66% for MLR models. The predictive capacity was more stable for the artificial neural networking model than the MLR models. It shows that ANN models are able to have a more tolerant capacity and are less affected by abnormal values or multicollinearity. It also allows for more reliable adaptability with desirable results [58].



Application of ANNs in PK and PD modeling has been shown to have increasing potential in the clinical setting. ANNs are able to incorporate experimental and evidence-based data to solve complex problems in the pharmaceutical field. They are an advantageous tool for learning, recognizing, and generalizing data that are useful in analysis and prediction. They provide the predictive tool needed to overcome any limitations from traditional to regression methods. The nonlinear versatility and adaptability associated with ANNs for PK modeling is proving to be successful as more studies are being conducted in the clinical setting.

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Clinical Applications of Artificial Neural Networks in Pharmacokinetic Modeling

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