Research Article  Open Access
Quantitative Assessment of the Physiological Parameters Influencing QT Interval Response to Medication: Application of Computational Intelligence Tools
Abstract
Human heart electrophysiology is complex biological phenomenon, which is indirectly assessed by the measured ECG signal. ECG trace is further analyzed to derive interpretable surrogates including QT interval, QRS complex, PR interval, and T wave morphology. QT interval and its modification are the most commonly used surrogates of the drug triggered arrhythmia, but it is known that the QT interval itself is determined by other nondrug related parameters, physiological and pathological. In the current study, we used the computational intelligence algorithms to analyze correlations between various simulated physiological parameters and QT interval. Terfenadine given concomitantly with 8 enzymatic inhibitors was used as an example. The equation developed with the use of genetic programming technique leads to general reasoning about the changes in the prolonged QT. For small changes of the QT interval, the drugrelated IKr and ICa currents inhibition potentials have major impact. The physiological parameters such as body surface area, potassium, sodium, and calcium ions concentrations are negligible. The influence of the physiological variables increases gradually with the more pronounced changes in QT. As the significant QT prolongation is associated with the drugs triggered arrhythmia risk, analysis of the role of physiological parameters influencing ECG seems to be advisable.
1. Introduction
Human heart electrophysiology is a complex biological phenomenon, which is indirectly assessed by the measured ECG (electrocardiography) signal and its derivatives. The latter, including QT interval, QRS complex, PR interval, and T wave morphology information, are main noninvasive clinical risk markers determining patent’s cardiac risk and are widely used in clinical practice for the diagnosis of cardiac disorders. Analysis of the electrographic biomarkers modification is also important from the drug development point of view, namely, assessment of drug cardiovascular safety, as it allows for quantification of drugs’ and drugs candidates’ influence on the human heart electrophysiology [1]. This is possible because of the wellknown correlation between the drugs triggered ionic currents disruption, ECG modification, and subsequent increase in the risk of arrhythmia occurrence [2]. Probably the best established and widely used predictor of the arrhythmia risk is the QT interval prolongation compared to the baseline (delta QT or dQT) [3]. Despite the criticism that the specificity of this proarrhythmia risk surrogate is not ideal, it is still commonly used in the drug development process as well as in the clinic.
The surface ECG is a representation of the electrical activity of cardiomyocytes. The QT interval reflects the ventricular action potential duration (APD) which is determined by the flow of ionic currents across the cell membrane. The ionic currents underlying ventricular depolarization and repolarization can be disrupted by many drugs that block ion channels or ion channels trafficking. Although inhibition of the hERG channel (human etheragogorelated gene) regulating the major repolarizing current in the heart, IKr (delayed inward potassium current), is the most common mechanism of QT prolongation [4, 5], it can also be caused by the drug triggered inhibition of other channels, that is, potassium (Kv7.1), sodium (Nav1.5), or calcium (Cav1.2) [6–9].
It is also known that, apart from the drug of interest, there are other parameters influencing QT interval duration. They can be divided into external (e.g., other medications taken concomitantly, which may potentiate cardiac risk by influencing the pharmacokinetics (PK) of QTprolonging drug leading to the increase in its concentration or by the additive impact on ion channels), and internal (physiological and pathological) parameters.
The current study aimed to analyze the data from multiple virtual clinical trials simulated with the use of the biophysically detailed model of human cardiac cells physiology. The endpoint of interest was QT interval length, and the analyzed independent parameters covered external and internal parameters.
2. Materials and Methods
2.1. Data Set
Population of virtual patients exposed to terfenadine alone or in combination with various metabolic inhibitors (clarithromycin, erythromycin, itraconazole, ketoconazole, fluconazole, fluoxetine, and paroxetine) during the simulated clinical trials was used to analyze factors influencing the observed interindividual variability [10–16]. Simcyp (version 14.1) platform was used for the PK simulations. Electrophysiological response to drug was simulated in ten TusscherNobleNoblePanfilov human ventricular cardiomyocyte model [17] implemented in Cardiac Safety Simulator™ (CSS v2.0, Certara USA, Inc.). The modeling procedure was described in detail in the recently published paper [18]. In brief, seven clinical studies focused on the electrophysiological consequences of the drugdrug interactions of terfenadine were mimicked in silico with the use of mechanistic models describing drugs pharmacokinetics and pharmacodynamics (PD). The inhibitors interacting with terfenadine covered strong, moderate, and weak inhibitors of CYP3A4dependent terfenadine metabolism and strong CYP2D6 inhibitors. The perpetrators have diverse propensity to block hERG channel and are associated with QT prolongation and TdP risk. Fluoxetine and paroxetine are also known to block other ionic currents influencing cardiomyocyte electrophysiology, that is, ICaL (late calcium current, Cav1.2) and ICaL (late calcium current, Cav1.2) with INa (peak sodium current, Nav1.5), respectively. The endpoint of interest was QTc modification: a QT interval prolongation (as compared against a baseline), corrected for the heart rate according to the Fridericia equation [19]. Developed PK model enabled both generation of individual patient data (drugs’ timeconcentration profiles with corresponding values of physiological parameters influencing PK, e.g., CYP abundance) and simulation of individual pseudoECG signals dependent on i.a. age, gender, and heart parameters.
A set of 48 factors influencing the obtained differences in QTc values were analyzed. This included human related parameters (demographic, anatomical, and physiological), drugrelated parameters (inhibition values of four main cardiac ionic currents), and studydependent parameters (time of the day when the drug was taken). All of the abovementioned parameters were generated with the use of Simcyp Simulator. The final data set consisted of 10,360 records representing QT interval durations for 63 patients taking terfenadine alone or with the concomitant drug in different time points of clinical studies [18]. The final data set consisted of 10,360 records and its summary is shown in Table 1.
 
Where CYP1A2, CYP2A6, CYP2B6, CYP2C8, CYP2C9, CYP2C18, CYP2C19, CYP2D6, CYP2E1, CYP2J2, CYP3A4, CYP3A5, CYP3A7, corresponding patients’ abundance of cytochromes in the liver [pmol/mg of protein]; Gut_CYP2C9, Gut_CYP2C19, Gut_CYP2D6, Gut_CYP2J2, Gut_CYP3A4, Gut_CYP3A5, corresponding patients’ abundance of cytochromes in the gut [nmol/small intestine]; Sex_Code, patients’ gender [male = 0/female = 1]; Age, patients’ age [years]; Weight, patients’ weight [kg]; Height, patients’ height [cm]; BSA, patients’ body surface area [m^{2}]; Brain_Weight, patients’ brain weight [g]; Kidney_Weight, patients’ kidney weight [g]; Liver_Weight, patients’ liver weight [g]; BMI, patients’ body mass index; Cardiac_Output, patients’ cardiac output [L/h]; Haematocrit, patients’ specific haematocrit [%]; HSA, AGP, patients’ specific level of human serum albumin and alfaacid glycoproteins in the plasma [g/L]; Serum_Creatinine, patients’ specific creatinine level [μmol/L]; GFR, the Glomerular Filtration Rates of the simulated individual (mL/min/1.73 m^{2}); Renal_Function, the ratio of individual’s GFR to that of the normal value of 120 mL/min/1.73 m^{2} for male or 130 mL/min/1.73 m^{2} for female; Cardiomyocyte_area, patients’ specific area of the cardiac myocyte [μm^{2}]; Cardiomyocyte_volume, patients’ specific volume of the cardiac myocyte [μm^{3}]; Sarcoplasmic_reticulum_volume, patients’ specific volume of the cardiac myocyte sarcoplasmic reticulum [μm^{3}]; Capacitance, patients’ specific cardiac myocyte electric capacitance [pF]; String_length, patients’ specific thickness of the left heart wall [cm]; K, Na, Ca2, patients’ specific concentration of ions in plasma [mM]; IKr_inhibition, IKs_inhibition, INa_inhibition, ICa_inhibition, patients’ and drugs’ specific ionic current inhibition; Stimulation_Period, time gaps between stimulaitons [ms]; dQTc, patients’ QTc interval modification as compared against baseline. 
Then the data set was preprocessed to overcome several potential pitfalls:(i)data set was split according to the 8fold crossvalidation scheme, in each fold the data belonging to the particular metabolic inhibitors was excluded; as a consequence the developed model was forced to predict the dQTc of the unknown combination of the terfenadinedrug interaction (noted as “8cv”), which mimics the reallife application for the unknown combination,(ii)noise addition to prevent models from overfitting,(iii)noised data records were produced numerically with ±5% amplitude for each variable value and two times more records number,(iv)linear scaling of the data in the range of was applied to match nonlinear activation functions of ANNs (Artificial Neural Networks).
2.2. Modeling
Modeling was carried out with the use of computational intelligence tools available as packages in the Open Source statistical environment [20], namely, fscaret [21], monmlp (Monotonic Artificial Neural Networks) [22], Cubist [23], randomForest (RF, Random Forest) [24], earth (MARS, Multivariate Adaptive Regression Splines) [25], rgp (Genetic Programming and Symbolic Regression) [26], and nloptr [27]. All models were of multipleinputsingleoutput (MISO) type. The whole procedure was carried out in the following steps (Figure 1):(i)reduction of the input vector based on feature ranking produced by fscaret,(ii)selection of the input vector yielding the lowest error among four types of models, namely: monmlp, Cubist, RF, and MARS,(iii)development of the mathematical equations with the use of the GP and symbolic regression based on the selected input vector,(iv)selection of the mathematical equation, optimization of its parameters and analysis of its variables on the differences in QTc values to create general conclusions regarding the terfenadinedrugs interaction.
Feature ranking obtained with the use of fscaret package of the R environment was employed to reduce the number of variables in the data set. The main advantages of the package are the vast number of available models for feature ranking creation, automation, and models verification based on the results obtained in earlier research, where the number of input variables was successfully reduced to 2% or 5% of the original vector [28, 29]. The fscaret work cycle involves training models, scaling each one according to the global performance, namely, mean squared error (MSE) or root mean squared error (RMSE), and summarizing results into the feature ranking. The main settings of the package were as follows: regression mode was turned on, timelimiting option (myTimeLimit) of single model development was set to 12 hours, and if possible all available functions were used. After the feature ranking was produced the cutoff points, which were limiting the number of the inputs, were selected according to the criteria that the decrease of the input’s importance is more than 5% of its sum.
Both linear and nonlinear methods such as Cubist, monmlp, RF, and MARS were selected for screening the input vector, mainly due to their low computational cost and effective generalization ability in the regression problems.
An environment tree based modeling approach utilized for the study was Cubist [23]. As a result of its application, the tree which consists of a set of linear models for each node is obtained. On a given training data a tree is generated which combines IFTHEN rules and linear regression models [30]. A maximum number of rules was fixed at 100, and the number of committees varied from 1 to 100.
Another tree based algorithm used was a Random Forest (RF) [31]. It is an ensemble learning method where multiple tree predictors are built on a randomly sampled vector of variables, and then they are merged to form one model. The sample distribution is kept same for all the trees [24]. The number of terminal nodes and trees in the single model varied from 10 to 1000. Random variables sampled for each tree were established from one to the maximum number of variables in an input vector.
Monotonic multilayer perceptrons (monmlp [22]) are generalized feed forward neural networks which are trained using nonlinear Newtoniantype minimization algorithm. The advantage of monmlp package is its ability to build models aggregated in expert committees. All created models were composed of two hidden layers, the number of neurons ranged from 4 to 50, and all models consisted of 10 ensemble networks. As a transition function hiperbolic tangent and linear function were applied to hidden and output layer, respectively. The number of iterations varied from 10 to 1000.
Multivariate adaptive regression splines (MARS) is an analysis introduced by Friedman in 1991 [32]. The model is a weighted sum of constant and basic functions multiplied by coefficients. The basic function in MARS is the hinge function. The function returns value if is greater than a constant, or 0 otherwise. The model is built in two steps. First, the model development starts from a single intercept and is extended iteratively by adding pairs of hinge functions. This process leads to model overfitting. Then the basic functions are removed from the model to improve generalization ability of the final model [33]. Earth package for R environment was used in the present work as an example of the multivariate adaptive regression splines method [25].
The goodness of fit was expressed as the normalized root mean squared error (NRMSE) (see (1)) and the coefficient of determination .
Equation (1) is as follows:where and are the observed and predicted values, respectively, is the data record number, is the total number of records, and and are the maximum and minimum observed values of dQTc.
The genetic programming (GP), in opposite to other algorithms, produces fully transparent models (whitebox) which can be expressed in a form of the mathematical equations. Apart from clear mathematical formulation of the model, GP also offers potential of automatic variables selection, thus further narrowing down the most important variables set obtained by fscaret. The GP and the symbolic regression mode available in the rgp package [26] of the Open Source statistical environment [20] were used in order to develop equations. Two heuristic strategies available as rgp options were applied concurrently:
(i) makeAgeFitnessComplexityParetoGpSearchHeuristic()
(ii) makeArchiveBasedParetoTournamentSearchHeuristic()
For both strategies all parameters were set to defaults.
Genetic programming (GP) is a method of automatic computer program creation. Lisp language was chosen as the main programming language for GP, because of its highly symboloriented structure. Therefore the algorithm was able to manipulate symbolic expressions to find a solution based on general problem definition [34].
A symbolic regression, which is based on evolutionary algorithms, was used during the research. Symbolic regression is a process of fitting the observed data by a mathematical formula. A chromosome encodes solution, namely, mathematical equation, which is further modified using genetic algorithms operations like crossover and mutations. The rgp package of environment was used in this work [26]. Population size was set to 100 and a total number of steps in evolution process were set to 100 million. During the evolution, after a predefined number of fitness function evaluations (1000 population size) an elite of solutions was tested with 8fold crossvalidation scheme to produce generalization error. The adjustable parameters of the equations were randomly reinitialized and fitted using multivariate optimization provided by nloptr package [27]. Additionally, a noised data set based on the whole database was introduced for model testing in order to determine its stability. The maximum length of a chromosome, parameter “individualSizeLimit” of rgp, which defines a maximum degree of complexity of the solution varied from 10 to 100. The goodness of fit for evolved solutions during evolution process was assessed with root mean square error (RMSE). After the modeling step the resulting equations were sorted according to their complexity, number of parameters, and the error obtained on the 8fold and noised data. The final model was selected according to multivariate criterion encompassing minimum complexity, the number of adjustable parameters, and generalization error (RMSE).
All scripts utilized in the study are available to download from “R scripts for multivariate analysis” resource page at SourceForge.net [35].
Computations were performed on the servers arranged in the grid structure and working under Linux operating systems control.
3. Results and Discussion
3.1. Results
The first stage of the research was to reduce the input vector based on the feature ranking produced by the fscaret package. According to the feature ranking created by fscaret, eight reduced input vectors containing 9, 10, 13, 14, 18, 19, and 23 independent variables were selected to perform modeling with the use of heuristic tools, namely, monmlp, Cubist, RF, and MARS. The results of the screening are presented in Table 1. The results obtained using the computational intelligence tools had an NRMSE of 8cv in a range from 3.8% to 6.2% (Table 2). The lowest generalization error was achieved for the model developed with Cubist algorithm trained on a vector with 18 inputs. The results obtained in this step indicate that there was a good potential for implementation of GP models.

Within this list, a vector of 14 inputs was selected for GP computations as it contained all crucial parameters related to the physiology (Table 3). Therefore expert knowledge was combined with the automated feature ranking tool for final crucial variables set. Further feature elimination was performed during the GP modeling and will be described later in the text. The most important parameters for dQTc included gender, weight, body surface area, cardiac output, CYPs abundance, electrolytes concentrations, and ionic currents inhibition (Table 3).

Equation (see (2)) derived from a data set consisting of 14 inputs (Table 3) yielded a generalization error in eightfold crossvalidation (NRMSE) of 3.97% and coefficient of determination of 0.923. The results were comparable to the previously developed best model (Cubist, 3.7%). Therefore it was considered as not overfitted. The equation was characterized by 4 parameters (see (2)). Moreover, during the evolution process, the GP algorithm further reduced the number of necessary variables by eliminating input numbers: 1, 11, 14, 20, 22, and 29 (Table 3). The simplified mathematical model retained eight input variables, yet its predictive performance was comparable to the more complex Cubist model.
Equation (2) is as follows:where dQTc is the difference in QTc value and , , , , , , , and correspond to the labels in Table 2. Based on the optimization on the whole data set the adjustable parameters of (2) were as follows: , , , and . Figure 2 shows predicted versus observed values for dQTc calculated according to (2).
To analyze the influence of each variable of (2) on the dQTc a response analysis was performed. Each time a variable was chosen and its values were iteratively changed in a range from minimum to maximum as in the data set. The values for the remaining variables were the first, the second, the third, the fourth, and the fifth quantile (0, 25, 50, 75, and 100%). As a result, the plots were drawn for each variable versus dQTc. The plots are presented in Figures 3–7.
The model was tested on the data extrapolated for two most pronounced channel inhibition effects, namely, IKr and ICa. The inhibition values for both channels were sampled in the range 0 to 1 with an increment of 0.01 setting all the remaining variables on their median values. The resulting dQTcF values were plotted as one channel versus another matching their inhibition values.
There is a strong linear relationship between the obtained results allowing concluding on the strengths of the observed effects. The same extent of ICa inhibition produces roughly an effect of twice the magnitude of the IKr inhibition. Since both effects are contradictory, it is important information for future drug development in regard to the safety of the therapy.
3.2. Discussion
The applied methodology, which is an adaptation of the CRISPDM protocol, confirmed the high quality of the developed model. Combination of feature selection tool (fscaret) and fast modeling techniques (Cubist, monmlp, RF, and MARS) allowed reducing the input vector by more than 50% of variables. Moreover, the obtained errors below 6.3% in the 8fold crossvalidation protocol lead to the conclusion that the developed models have not only the interpolation but also the extrapolation ability. Additionally, the equation development process and its selection assure the high quality of the GP model.
Further analysis of the equation developed by the GP technique leads to general reasoning about the changes in dQTc. It is clearly depicted that when dependent variables have small values, from the first and the second quantile (Figures 3 and 4), the differences in QTc are influenced by the IKr and ICa inhibition potentials. Moreover, the physiological parameters such as body surface area, potassium, sodium, and calcium ions concentrations have very little or none impact on the dQTc. The influence of these variables increases gradually from quantile third to fourth (Figures 5 and 6) and the highest changes in dQTc are observed when independent variables are in the fifth quantile (Figure 7). Within the data range IKs and INa inhibition currents have limited impact on the differences in QTc values (Figures 3–7). The influence of the physiological variables increases gradually with the more pronounced changes in QT. As the significant QT prolongation is associated with the drugs triggered arrhythmia risk, analysis of the role of physiological parameters influencing ECG seems to be advisable.
It is also worth noting that all the abovepresented results, except the data set, were obtained with the use of the Open Source software, namely, statistical environment and external packages. This study is an example of how Open Source might be exploited to create sophisticated models and modeling strategies. Use of these tools is worth consideration to provide reliable and reproducible solutions at the low cost of their development.
4. Conclusions
In this work, we have shown how data processing and exploration with various computational intelligence techniques reveal hidden relationships suitable for identification of physical mechanisms relevant to the electrophysiological properties of the human cardiomyocyte. Moreover, empirical development of mathematical equations provides a convenient way to the formulation of scientific hypotheses both of the qualitative and quantitative nature. The latter was demonstrated i.a. with estimation of the relative impact of the IKr versus ICa inhibition in their antagonist influence on the QT prolongation (Figure 8).
Conflicts of Interest
The authors declare that there are conflicts of interest regarding the publication of this article; Sebastian Polak is an employee of Simcyp (part of Certara) which develops Cardiac Safety Simulator and Simcyp platform used in the current study.
Acknowledgments
This work was supported by the Polish National Science Center (DEC2013/11/D/NZ7/01583).
References
 R. M. Lester and J. Olbertz, “Early drug development: assessment of proarrhythmic risk and cardiovascular safety: the age of repolarization cardiac toxicity,” Expert Review of Clinical Pharmacology, vol. 9, no. 12, pp. 1611–1618, 2016. View at: Publisher Site  Google Scholar
 C. van Noord, M. Eijgelsheim, and B. H. C. Stricker, “Drug and nondrugassociated QT interval prolongation,” British Journal of Clinical Pharmacology, vol. 70, no. 1, pp. 16–23, 2010. View at: Publisher Site  Google Scholar
 D. M. Roden, “Druginduced prolongation of the QT interval,” The New England Journal of Medicine, vol. 350, no. 10, pp. 1013–1022, 2004. View at: Publisher Site  Google Scholar
 M.L. Roy, R. Dumaine, and A. M. Brown, “HERG, a primary human ventricular target of the nonsedating antihistamine terfenadine,” Circulation, vol. 94, no. 4, pp. 817–823, 1996. View at: Publisher Site  Google Scholar
 A. M. Brown, “hERG Block, QT Liability and Sudden Cardiac Death,” Novartis Foundation Symposia, vol. 266, pp. 118–131, 2005. View at: Google Scholar
 K. S. Lee, “Ibutilide, a new compound with potent class III antiarrhythmic activity, activates a slow inward Na+ current in guinea pig ventricular cells,” The Journal of Pharmacology and Experimental Therapeutics, vol. 262, no. 1, pp. 99–108, 1992. View at: Google Scholar
 C. T. January and J. M. Riddle, “Early afterdepolarizations: mechanism of induction and block. A role for Ltype Ca^{2+} current,” Circulation Research, vol. 64, no. 5, pp. 977–990, 1989. View at: Publisher Site  Google Scholar
 B. Szabo, R. Sweidan, C. V. Rajagopalan, and R. Lazzara, “Role of Na+:Ca^{2+} exchange current in Cs+induced early afterdepolarizations in Purkinje fibers,” Journal of Cardiovascular Electrophysiology, vol. 5, no. 11, pp. 933–944, 1994. View at: Publisher Site  Google Scholar
 D. M. Roden, R. Lazzara, M. Rosen, P. J. Schwartz, J. Towbin, and G. Michael Vincent, “Multiple mechanisms in the longQT syndrome: current knowledge, gaps, and future directions,” Circulation, vol. 94, no. 8, pp. 1996–2012, 1996. View at: Publisher Site  Google Scholar
 P. K. Honig, D. C. Wortham, K. Zamani, D. P. Conner, J. C. Mullin, and L. R. Cantilena, “Terfenadineketoconazole interaction: pharmacokinetic and electrocardiographic consequences,” Journal of the American Medical Association, vol. 269, no. 12, pp. 1513–1518, 1993. View at: Publisher Site  Google Scholar
 P. K. Honig, R. L. Woosley, K. Zamani, D. P. Conner, and L. R. Cantilena, “Changes in the pharmacokinetics and electrocardiographic pharmacodynamics of terfenadine with concomitant administration of erythromycin,” Clinical Pharmacology & Therapeutics, vol. 52, no. 3, pp. 231–238, 1992. View at: Publisher Site  Google Scholar
 P. K. Honig, D. C. Wortham, R. Hull, K. Zamani, J. E. Smith, and L. R. Cantilena, “Itraconazole affects single‐dose terfenadine pharmacokinetics and cardiac repolarization pharmacodynamics,” The Journal of Clinical Pharmacology, vol. 33, no. 12, pp. 1201–1206, 1993. View at: Publisher Site  Google Scholar
 P. K. Honig, D. C. Wortham, K. Zamani, J. C. Mullin, D. P. Conner, and L. R. Cantilena, “The effect of fluconazole on the steady‐state pharmacokinetics and electrocardiographic pharmacodynamics of terfenadine in humans,” Clinical Pharmacology & Therapeutics, vol. 53, no. 6, pp. 630–636, 1993. View at: Publisher Site  Google Scholar
 P. K. Honig, D. C. Wortham, K. Zamani, and L. R. Cantilena, “Comparison of the effect of the macrolide antibiotics erythromycin, clarithromycin and azithromycin on terfenadine steadystate pharmacokinetics and electrocardiographic parameters,” Drug Investigation, vol. 7, no. 3, pp. 148–156, 1994. View at: Publisher Site  Google Scholar
 R. F. Bergstrom, M. J. Goldberg, B. J. Cerimele, and B. L. Hatcher, “Assessment of the potential for a pharmacokinetic interaction between fluoxetine and terfenadine,” Clinical Pharmacology & Therapeutics, vol. 62, no. 6, pp. 643–651, 1997. View at: Publisher Site  Google Scholar
 D. E. Martin, B. D. Zussman, D. E. Everitt, L. J. Benincosa, R. C. Etheredge, and D. K. Jorkasky, “Paroxetine does not affect the cardiac safety and pharmacokinetics of terfenadine in healthy adult men,” Journal of Clinical Psychopharmacology, vol. 17, no. 6, pp. 451–459, 1997. View at: Publisher Site  Google Scholar
 K. H. W. J. ten Tusscher, D. Noble, P. J. Noble, and A. V. Panfilov, “A model for human ventricular tissue,” American Journal of PhysiologyHeart and Circulatory Physiology, vol. 286, no. 4, pp. H1573–H1589, 2004. View at: Publisher Site  Google Scholar
 B. Wiśniowska and S. Polak, “Virtual clinical trial toward polytherapy safety assessment: combination of physiologically based pharmacokinetic/pharmacodynamicbased modeling and simulation approach with drugdrug interactions involving terfenadine as an example,” Journal of Pharmaceutical Sciences, vol. 105, no. 11, pp. 3415–3424, 2016. View at: Publisher Site  Google Scholar
 B. Vandenberk, E. Vandael, T. Robyns et al., “Which QT correction formulae to use for QT monitoring?” Journal of the American Heart Association, vol. 5, no. 6, Article ID e003264, 2016. View at: Publisher Site  Google Scholar
 R Core Team, “R: A language and environment for statistical computing,” 2015, http://www.Rproject.org/. View at: Google Scholar
 J. Szlek, A. Pacławski, R. Llau, R. Jachowicz, and A. Mendyk, “Heuristic modeling of macromolecule release from PLGA microspheres,” International Journal of Nanomedicine, vol. 8, pp. 4601–4611, 2013. View at: Publisher Site  Google Scholar
 A. J. Cannon, “monmlp: Monotone multilayer perceptron neural network,” 2017, http://cran.rproject.org/web/packages/monmlp/index.html. View at: Google Scholar
 M. Kuhn, S. Weston, C. Keefer, and N. Coulter, “C code for Cubist by Ross Quinlan. Cubist: Rule and InstanceBased Regression Modeling,” 2017, http://CRAN.Rproject.org/package=Cubist. View at: Google Scholar
 L. Breiman, “Random forests,” Machine Learning, vol. 45, no. 1, pp. 5–32, 2001. View at: Google Scholar
 S. Milborrow, “Earth: Multivariate Adaptive Regression Splines,” 2017, http://cran.rproject.org/web/packages/earth/index.html. View at: Google Scholar
 O. Flasch, O. Mersmann, T. BartzBeielstein, and J. Stork, “rgp: R genetic programming framework,” 2011, R package version 0.24, http://CRAN.Rproject.org/package=rgp. View at: Google Scholar
 J. Ypma, nloptr: R interface to NLopt, 2017, http://cran.rproject.org/web/packages/nloptr/index.html.
 B. Wiśniowska, A. Mendyk, J. Szlek, M. Kołaczkowski, and S. Polak, “Enhanced QSAR models for drugtriggered inhibition of the main cardiac ion currents,” Journal of Applied Toxicology, vol. 35, no. 9, pp. 1030–1039, 2015. View at: Publisher Site  Google Scholar
 J. Szlęk, A. Pacławski, R. Lau, R. Jachowicz, P. Kazemi, and A. Mendyk, “Empirical search for factors affecting mean particle size of PLGA microspheres containing macromolecular drugs,” Computer Methods and Programs in Biomedicine, vol. 134, pp. 137–147, 2016. View at: Publisher Site  Google Scholar
 J. R. Quinlan, “Learning with continuous classes,” in Proceedings of the 5th Australian Joint Conference on Artificial Intelligence, pp. 343–348, 1992. View at: Google Scholar
 A. Liaw and M. Wiener, “Classification and regression by randomforest,” The R Journal, vol. 2, no. 3, pp. 18–22, 2002. View at: Google Scholar
 J. H. Friedman, “Multivariate adaptive regression splines,” The Annals of Statistics, vol. 19, no. 1, pp. 1–67, 1991. View at: Publisher Site  Google Scholar  MathSciNet
 W. Zhang and A. T. C. Goh, “Multivariate adaptive regression splines and neural network models for prediction of pile drivability,” Geoscience Frontiers, vol. 7, no. 1, pp. 45–52, 2016. View at: Publisher Site  Google Scholar
 J. R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press, Massachusetts, Mass, USA, 1992.
 “R scripts for multivariate analysis,” 2017, https://sourceforge.net/projects/rscriptsmultivariate/files/. View at: Google Scholar
Copyright
Copyright © 2018 Sebastian Polak et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.