Review of the Simulators used in Pharmacology Education and Statistical Models when creating the Simulators

Toshiaki Ara; Hiroyuki Kitamura

doi:10.51094/jxiv.991

##article.authors##

Toshiaki Ara Department of Pharmacology, Matsumoto Dental University
Hiroyuki Kitamura Matsumoto Dental University Hospital, Department of Oral Diagnostics and Comprehensive Dentistry

DOI:

https://doi.org/10.51094/jxiv.991

Keywords:

pharmacological education, animal use alternative, simulator, statistical model, sigmoid curve

Abstract

Animal experiments have long been used as an educational tool in pharmacological education; however, from the perspective of animal welfare, it is necessary to decrease the number of animals used. In this review, we describe free downloadable and commercial simulators that are currently used in pharmacological education. Furthermore, we introduce two strategies to create simulators of animal experiments: (1) bioassay, and (2) experiments that measure the reaction time. We also describe five sigmoid curves (logistic curve, cumulative distribution function [CDF] of normal distribution, Gompertz curve, von Bertalanffy curve, and CDF of Weibull curve) to fit the results and their inverse functions. Using this strategy, it is possible to create a simulator that calculates the reaction time following drug administration. Moreover, we introduce a statistical model for local anesthetic agents using hierarchical Bayesian modeling. Considering the correlation among estimated parameters, we suggest it is possible to create simulators that give results more similar to those of animal experiments.

Conflicts of Interest Disclosure

The authors declare that they have no competing interest

Downloads *Displays the aggregated results up to the previous day.

Download data is not yet available.

Author Biography

Hiroyuki Kitamura, Matsumoto Dental University Hospital, Department of Oral Diagnostics and Comprehensive Dentistry

松本歯科大学病院・総合診療室

References

Council, N.R. Guide for the Care and Use of Laboratory Animals: Eighth Edition; The National Academies Press: Washington, DC, 2011. https://doi.org/10.17226/ 12910.

Ara, T.; Kitamura, H. Development of a Predictive Statistical Pharmacological Model for Local Anesthetic Agent Effects with Bayesian Hierarchical Model Parameter Estimation. Medicines 2023, 10, 61. https://doi.org/10.3390/ medicines10110061.

Ara, T.; Kitamura, H. Improvement of local anesthetics agents' simulation using Monte Carlo simulation considering correlation among parameters. BioInfoMedicines 2024, 4, 2133–2148. https://doi.org/10.3390/ biomedinformatics4040114.

Ezeala, C.C. Integration of computer-simulated practical exercises into undergladuate medical pharmacology education at Mulungushi University, Zambia. Journal of educational evaluation for health professions 2020, 17. https://doi.org/ 10.3352/jeehp.2020.17.8.

Andrews, L.B.; Barta, L. Simulation as a Tool to Illustrate Clinical Pharmacology Concepts to Healthcare Program Learners. Current pharmacology reports 2020, 6, 182–191. https://doi.org/10.1007/s40495-020-00221-w.

University of Strathclyde. Strathclyde Pharmacology Simulations. http://spider.science.strath.ac.uk/sipbs/page.php?page=software_sims [accessed on 2024 Oct 28].

Borghardt, J.M.; Weber, B.; Staab, A.; Kloft, C. Pharmacometric Models for Characterizing the Pharmacokinetics of Orally Inhaled Drugs. AAPS J 2015, 14, 853–870. https://doi.org/10.1208/s12248-015-9760-6.

Ara, T. simla-ts (ver 2.1.0), 2024. https://toshi-ara.github.io/simla-ts/sim_ local_anesthetics.html [accessed on 2024 Oct 23], https://doi.org/10.5281/ zenodo.13982183.

eGrid Corporation. Pharmaco-PICOS: Pharmacological practice of intestine and cardiovascular organ simulator. https://pharmaco-picos.education [accessed on 2024 Oct 28].

ERISA. BMP-VR: Basic Medicine Practice-Virtual Reality. https://www.erisa. co.jp/product/ (in Japanese); inteview: https://jstories.media/article/ animal-experiments [accessed on 2024 Oct 28].

Certara. SimcypTM: PBPK Tech-driven Services Predict clinical outcomes from virtual populations. https://www.certara.com/services/simcyp-pbpk [accessed on 2024 Oct 28].

Plus, S. PKPlusTM Module extends GastroPlus®: PBPK & PBBM modeling software. https://www.simulations-plus.com/software/gastroplus/pk-models [accessed on 2024 Oct 28].

van Hagen, M.A.E.; Ducro, B.J.; van den Broek, J.; Knol, B.W. Incidence, risk factors, and heritability estimates of hind limb lameness caused by hip dysplasia in a birth cohort of boxers. American Journal of Veterinary Research 2005, 66, 307–312. https://doi.org/10.2460/ajvr.2005.66.307.

Kim, J.; Park, Y.R.; Lee, J.H.; Lee, J.H.; Kim, Y.H.; Huh, J.W. Development of a Real-Time Risk Prediction Model for In-Hospital Cardiac Arrest in Critically Ill Patients Using Deep Learning: Retrospective Study. JMIR Medical Informatics 2020, 8, e16349. https://doi.org/10.2196/16349.

Lord, P.F.; Kapp, D.S.; Hayes, T.; Weshler, Z. Production of systemic hyperthermia in the rat. European Journal of Cancer and Clinical Oncology 1984, 20, 1079–1085. https://doi.org/10.1016/0277-5379(84)90111-1.

Gonsowski, C.T.; Laster, M.J.; Eger, E.I.; Ferrell, L.D.; Kerschmann, R.L. Toxicity of Compound A in Rats: Effect of a 3-Hour Administration. Anesthesiology 1994, 80, 556–565. https://doi.org/10.1097/00000542-199403000-00012.

Peduzzi, P.; Concato, J.; Kemper, E.; Holford, T.R.; Feinstein, A.R. A simulation study of the number of events per variable in logistic regression analysis. Journal of Clinical Epidemiology 1996, 49, 1373–1379. https://doi.org/10.1016/ s0895-4356(96)00236-3.

Li, J.; Shan, X.; Chen, Y.; Xu, C.; Tang, L.; Jiang, H. Fitting of Growth Curves and Estimation of Genetic Relationship between Growth Parameters of Qianhua Mutton Merino. Genes 2024, 15, 390. https://doi.org/10.3390/genes15030390.

Anellis, A.; Werkowski, S. Estimation of Radiation Resistance Values of Microorganisms in Food Products. Applied Microbiology 1968, 16, 1300–1308. https: //doi.org/10.1128/am.16.9.1300-1308.1968.

Little, R.A. Resistance to post-traumatic fluid loss at different ages. British journal of experimental pathology 1972, 53, 341–346.

Taylor, S.E.; Dorris, R.L. Modification of local anesthetic toxicity by vasoconstrictors. Anesthesia progress 1989, 36, 79–87.

Verma, S.S.; Gupta, R.K.; Nayar, H.S.; Rai, R.M. Gompertz curve in physiology: an application. Indian J Physiol Pharmacol 1982, 26, 47–53.

Vaghi, C.; Rodallec, A.; Fanciullino, R.; Ciccolini, J.; Mochel, J.P.; Mastri, M.; Ebos, J.M.L.; Benzekry, S. Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors. PLoS computational biology. PLoS computational biology 2020, 16, e1007178. https://doi.org/10.1371/journal.pcbi.1007178.

B.F., P.; N.A., C. A new method of fitting the von Bertalanffy growth curve using data on the whelk Dicathais. Growth 1968, 32, 317–329.

Kühleitner, M.; Brunner, N.; Nowak, W.G.; Renner-Martin, K.; Scheicher, K. Bestfitting growth curves of the von Bertalanffy-Pütter type. Poultry Science 2019, 98, 3587–3592. https://doi.org/10.3382/ps/pez122.

Kühleitner, M.; Brunner, N.; Nowak, W.G.; Renner-Martin, K.; Scheicher, K. Best fitting tumor growth models of the von Bertalanffy-PütterType. BMC Cancer 2019, 12, 683. https://doi.org/10.1186/s12885-019-5911-y.

Lee, L.; Atkinson, D.; Hirst, A.G.; Cornell, S.J. A new framework for growth curve fitting based on the von Bertalanffy Growth Function. Scientific Reports 2020, 10, 7953. https://doi.org/10.1038/s41598-020-64839-y.

Kuurman, W.; Bailey, B.; Koops, W.; Grossman, M. A model for failure of a chicken embryo to survive incubation. Poultry Science 2003, 82, 214–222. https://doi. org/https://doi.org/10.1093/ps/82.2.214.

Gil-Pozo, A.; Astudillo-Rubio, D.; Álvaro Ferrando Cascales.; Inchingolo, F.; Hirata, R.; Sauro, S.; Delgado-Gaete, A. Effect of gastric acids on the mechanical properties of conventional and CAD/CAM resin composites - An in-vitro study. Journal of the Mechanical Behavior of Biomedical Materials 2024, 155, 106565. https://doi.org/https://doi.org/10.1016/j.jmbbm.2024.106565.

Verhulst, P.F. Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Bruxelles; Vol. 18, 1845; p. 8.

Bliss, C.I. The Method of Probits. Science 1934, 79, 38–39. https://doi.org/10. 1126/science.79.2037.38.

Bliss, C.I. The Method of Probits—A Correction. Science 1934, 79, 409–410. https: //doi.org/10.1126/science.79.2053.409.

Epremian, E.; Mehl, R.F. Investigation of statistical nature of fatigue properties. National Advisory Committee for Aeronautics 1952, Technical Note 2719.

Ritteri, J.; Flower, R.; Henderson, G.; Loke, Y.K.; MacEwan, D.; Rang, H. Rang & Dale’s Pharmacology, 9th Edition; Elsevier: Amsterdam, Nederland, 2019.

Brunton, L.; Knollman, B.C. Pharmacological Basis of Therapeutics, 14th Edition; McGraw-Hill Education: New York City, NY, 2022.

Golan, D.E.; Tashjian Jr., A.H.; Armstrong, E.J.; Armstrong, A.W. Principles of Clinical Pharmacology: The Pathophysiologic Basis of Drug Therapy, 3rd Edition; Lippincott Williams & Wilkins: Philadelphia, PA, 2011.

Gompertz, B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London 1825, 115, 513–585. https: //doi.org/10.1098/rstl.1825.0026.

Winsor, C.P. The Gompertz Curve as a Growth Curve. Proc Natl Acad Sci U S A 1932, 18, 1–8. https://doi.org/10.1073/pnas.18.1.1.

von Bertalanffy, L. Untersuchungen Über die Gesetzlichkeit des Wachstums. I. Teil: Allgemeine Grundlagen der Theorie; Mathematische und physiologische Gesetzlichkeiten des Wachstums bei Wassertieren. Roux’ Archiv f. Entwicklungsmechanik 1934, 131, 613–652. https://doi.org/10.1007/BF00650112.

Weibull, W. The Statistical Theory of the Strength of Materials. Ingeniors Vetenskaps Academy Handlingar (151). Stockholm: Generalstabens Litografiska Anstalts Förlag 1939, pp. 1–45.

Rosin, P.; Rammler, E. The Laws Governing the Fineness of Powdered Coal. Journal of the Institute of Fuel 1933, 7, 29–36.

Yada, S.; Hamada, C. Application of Bayesian hierarchical models for phase I/II clinical trials in oncology. Pharmaceutical Statistics 2017, 16, 114–121. https:// doi.org/10.1002/pst.1793.

Fouarge, E.; Monseur, A.; Boulanger, B.; Annoussamy, M.; Seferian, A.M.; Lucia, S.D.; Lilien, C.; Thielemans, L.; Paradis, K.; Cowling, B.S.; et al. Hierarchical Bayesian modelling of disease progression to inform clinical trial design in centronuclear myopathy. Orphanet Journal of Rare Diseases 2021, 16, 3. https: //doi.org/10.1186/s13023-020-01663-7.

Haber, L.T.; Reichard, J.F.; Henning, A.K.; Dawson, P.; Chinthrajah, R.S.; Sindher, S.B.; Long, A.; Vincent, M.J.; Nadeau, K.C.; Allen, B.C. Bayesian hierarchical evaluation of dose-response for peanut allergy in clinical trial screening. Food and Chemical Toxicology 2021, 151. https://doi.org/10.1016/j.fct.2021.112125.

Curigliano, G.; Gelderblom, H.; Mach, N.; Doi, T.; Tai, D.; Forde, P.M.; Sarantopoulos, J.; Bedard, P.L.; Lin, C.C.; Hodi, F.S.; et al. Phase I/Ib Clinical Trial of Sabatolimab, an Anti-TIM-3 Antibody, Alone and in Combination with Spartalizumab, an Anti-PD-1 Antibody, in Advanced Solid Tumors. Clinical Cancer Research 2021, 27, 3620–3629. https://doi.org/10.1158/1078-0432.ccr-20-4746.

Gotuzzo, A.G.; Piles, M.; Della-Flora, R.P.; Germano, J.M.; Reis, J.S.; Tyska, D.U.; Dionello, N.J.L. Bayesian hierarchical model for comparison of different nonlinear function and genetic parameter estimates of meat quails. Poultry Science 2019, 98, 1601–1609. https://doi.org/10.3382/ps/pey548.

Paun, I.; Husmeier, D.; Hopcraft, J.G.C.; Masolele, M.M.; Torney, C.J. Inferring spatially varying animal movement characteristics using a hierarchical continuous-time velocity model. Ecology letters 2022, 25, 2726–2738. https: //doi.org/10.1111/ele.14117.

Ramos, A.N.; Fenton, F.H.; Cherry, E.M. Bayesian inference for fitting cardiac models to experiments: estimating parameter distributions using Hamiltonian Monte Carlo and approximate Bayesian computation. Medical & Biological Engineering & Computing 2023, 61, 75–95. https://doi.org/10.1007/ s11517-022-02685-y.

Yang, W.; Tempelman, R.J. A Bayesian antedependence model for whole genome prediction. Genetics 2012, 190, 1491–1501. https://doi.org/10.1534/genetics. 111.131540.

Selle, M.L.; Steinsland, I.; Lindgren, F.; Brajkovic, V.; Cubric-Curik, V.; Gorjanc, G. Hierarchical Modelling of Haplotype Effects on a Phylogeny. Frontiers in Genetics 2021, 11. https://doi.org/10.3389/fgene.2020.531218.

Mukaddim, R.A.; Meshram, N.H.; Mitchell, C.C.; Varghese, T. Hierarchical Motion Estimation With Bayesian Regularization in Cardiac Elastography: Simulation and In Vivo Validation. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 2019, 66, 1708–1722. https://doi.org/10.1109/tuffc.2019. 2928546.

Andrews, L.C. Special functions of mathematics for engineers, Second ed.; SPIE Press, 1998; p. 110.

Muller, R. Sequence A007680 in the On-Line Encyclopedia of Integer Sequences (n.d.). https://oeis.org/A007680 [accessed on 2024 Nov 11].

Abramowitz, M.; Stegun, I.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th edition; 1972. https://personal.math.ubc. ca/~cbm/aands/index.htm [accessed on 2024 Nov 9].

Carlitz, L. The inverse of the error function. Pacific Journal of Mathematics 1963, 13, 459–470.

Toda, H. An Optimal Rational Approximation for Normal deviates for Digital Computers. Bull Electrotech Lab 1967, 31, 1259–1270.

Guennebaud, G.; Jacob, B.; et al. Eigen v3, 2010. http://eigen.tuxfamily.org [accessed on 2024 Nov 11].

Genz, A.; Bretz, F. Computation of Multivariate Normal and t Probabilities; Lecture Notes in Statistics, Springer-Verlag: Heidelberg, 2009.

Harris, C.R.; Millman, K.J.; van der Walt, S.J.; Gommers, R.; Virtanen, P.; Cournapeau, D.; Wieser, E.; Taylor, J.; Berg, S.; Smith, N.J.; et al. Array programming with NumPy. Nature 2020, 585, 357–362. https://doi.org/10.1038/ s41586-020-2649-2.

Weissmann, B. multivariate-normal (v0.1.2): A pure-javascript port of NumPy’s random.multivariate_normal, for Node.js and the browser, 2023. https://www. npmjs.com/package/multivariate-normal.