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Reduction of quantitative systems pharmacology models using artificial neural networks

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Abstract

Quantitative systems pharmacology models are often highly complex and not amenable to further simulation and/or estimation analyses. Model-order reduction can be used to derive a mechanistically sound yet simpler model of the desired input–output relationship. In this study, we explore the use of artificial neural networks for approximating an input–output relationship within highly dimensional systems models. We illustrate this approach using a model of blood coagulation. The model consists of two components linked together through a highly dimensional discontinuous interface, which creates a difficulty for model reduction techniques. The proposed approach enables the development of an efficient approximation to complex models with the desired level of accuracy. The technique is applicable to a wide variety of models and provides substantial speed boost for use of such models in simulation and control purposes.

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References

  1. Bai JPF, Earp JC, Pillai VC (2019) Translational quantitative systems pharmacology in drug development: from current landscape to good practices. AAPS J 21(4):72. https://doi.org/10.1208/s12248-019-0339-5

    Article  PubMed  Google Scholar 

  2. Sadekar S, Figueroa I, Tabrizi M (2015) Antibody drug conjugates: application of quantitative pharmacology in modality design and target selection. AAPS J 17(4):828–836. https://doi.org/10.1208/s12248-015-9766-0

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. Betts AM, Haddish-Berhane N, Tolsma J, Jasper P, King LE, Sun Y, Chakrapani S, Shor B, Boni J, Johnson TR (2016) Preclinical to clinical translation of antibody-drug conjugates using PK/PD modeling: a retrospective analysis of inotuzumab ozogamicin. AAPS J 18(5):1101–1116. https://doi.org/10.1208/s12248-016-9929-7

    Article  CAS  PubMed  Google Scholar 

  4. Wajima T, Isbister GK, Duffull SB (2009) A comprehensive model for the humoral coagulation network in humans. Clin Pharmacol Ther 86(3):290–298. https://doi.org/10.1038/clpt.2009.87

    Article  CAS  PubMed  Google Scholar 

  5. Peterson MC, Riggs MM (2010) A physiologically based mathematical model of integrated calcium homeostasis and bone remodeling. Bone 46(1):49–63. https://doi.org/10.1016/j.bone.2009.08.053

    Article  CAS  PubMed  Google Scholar 

  6. Johansen AM (2010) Monte carlo methods. In: Peterson P, Baker E, McGaw B (eds) International encyclopedia of education, 3rd edn. Elsevier, Oxford, pp 296–303. https://doi.org/10.1016/B978-0-08-044894-7.01543-8

    Chapter  Google Scholar 

  7. Derbalah A, Al-Sallami H, Hasegawa C, Gulati A, Duffull SB (2020) A framework for simplification of quantitative systems pharmacology models in clinical pharmacology. Br J Clin Pharmacol. https://doi.org/10.1111/bcp.14451

    Article  PubMed  Google Scholar 

  8. Hasegawa C, Duffull SB (2017) Selection and qualification of simplified QSP models when using model order reduction techniques. AAPS J 20(1):2. https://doi.org/10.1208/s12248-017-0170-9

    Article  CAS  PubMed  Google Scholar 

  9. Snowden TJ, van der Graaf PH, Tindall MJ (2018) Model reduction in mathematical pharmacology. J Pharmacokinet Pharmacodyn 45(4):537–555. https://doi.org/10.1007/s10928-018-9584-y

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Gulati A, Faed JM, Isbister GK, Duffull SB (2015) Application of adaptive DP-optimality to design a pilot study for a clotting time test for enoxaparin. Pharm Res 32(10):3391–3402. https://doi.org/10.1007/s11095-015-1715-1

    Article  CAS  PubMed  Google Scholar 

  11. Mentré F, Friberg LE, Duffull S, French J, Lauffenburger DA, Li L, Mager DE, Sinha V, Sobie E, Zhao P (2020) Pharmacometrics and systems pharmacology 2030. Clin Pharmacol Ther 107(1):76–78. https://doi.org/10.1002/cpt.1683

    Article  PubMed  Google Scholar 

  12. Hasegawa C, Duffull SB (2018) Automated scale reduction of nonlinear QSP models with an illustrative application to a bone biology system. CPT Pharm Syst Pharmacol 7(9):562–572. https://doi.org/10.1002/psp4.12324

    Article  CAS  Google Scholar 

  13. Gulati A, Faed JM, Isbister GK, Duffull SB (2012) Development and evaluation of a prototype of a novel clotting time test to monitor enoxaparin. Pharm Res 29(1):225–235. https://doi.org/10.1007/s11095-011-0537-z

    Article  CAS  PubMed  Google Scholar 

  14. Gulati A, Isbister G, Duffull S (2014) Scale reduction of a systems coagulation model with an application to modeling pharmacokinetic-pharmacodynamic data. CPT Pharm Syst Pharmacol 3(1):90. https://doi.org/10.1038/psp.2013.67

    Article  CAS  Google Scholar 

  15. Ooi Q-X, Wright DFB, Isbister GK, Duffull SB (2018) A factor VII-based method for the prediction of anticoagulant response to warfarin. Sci Rep 8(1):12041. https://doi.org/10.1038/s41598-018-30516-4

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Nakano R, Saito K (2002) Discovering polynomials to fit multivariate data having numeric and nominal variables. In: Arikawa S, Shinohara A (eds) Progress in discovery science: final report of the japanese dicsovery science project. Springer, Berlin, Heidelberg, pp 482–493. https://doi.org/10.1007/3-540-45884-0_36

    Chapter  Google Scholar 

  17. Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Netw 4(2):251–257. https://doi.org/10.1016/0893-6080(91)90009-T

    Article  Google Scholar 

  18. Rayas-Sánchez JE (2013) Artificial neural networks and space mapping for EM-based modeling and design of microwave circuits. In: Koziel S, Leifsson L (eds) Surrogate-based modeling and optimization: applications in engineering. Springer, New York, pp 147–169. https://doi.org/10.1007/978-1-4614-7551-4_7

    Chapter  Google Scholar 

  19. Snoek J, Rippel O, Swersky K, Kiros R, Satish N, Sundaram N, Patwary M, Prabhat M, Adams R (2015) Scalable bayesian optimization using deep neural networks. In: International conference on machine learning. pp 2171–2180

  20. Kani JN, Elsheikh AH (2017) DR-RNN: a deep residual recurrent neural network for model reduction. arXiv preprint arXiv:170900939

  21. Derbalah A, Duffull S, Moynihan K, Al-Sallami H (2020) The influence of haemostatic system maturation on the dose-response relationship of unfractionated heparin. Clin Pharmacokinet. https://doi.org/10.1007/s40262-020-00949-0

    Article  PubMed  Google Scholar 

  22. Sy SKB, Asin-Prieto E, Derendorf H, Samara E (2014) Predicting pediatric age-matched weight and body mass index. AAPS J 16(6):1372–1379. https://doi.org/10.1208/s12248-014-9657-9

    Article  PubMed  PubMed Central  Google Scholar 

  23. Prout TA, Zilcha-Mano S, Aafjes-van Doorn K, Békés V, Christman-Cohen I, Whistler K, Kui T, Di Giuseppe M (2020) Identifying Predictors of psychological distress during COVID-19: a machine learning approach. Front Psychol. https://doi.org/10.3389/fpsyg.2020.586202

    Article  PubMed  PubMed Central  Google Scholar 

  24. Svozil D, Kvasnicka V, Jí P (1997) Introduction to multi-layer feed-forward neural networks. Chemom Intell Lab Syst 39(1):43–62. https://doi.org/10.1016/S0169-7439(97)00061-0

    Article  CAS  Google Scholar 

  25. Da Silva IN, Spatti DH, Flauzino RA, Liboni LHB, dos Reis Alves SF (2017) Artificial neural networks. Springer, Cham

    Book  Google Scholar 

  26. Lu Z, Pu H, Wang F, Hu Z, Wang L (2017) The expressive power of neural networks: a view from the width. In: Advances in neural information processing systems. pp 6231–6239

  27. Parmar VP, Kumbharana C (2015) Comparing linear search and binary search algorithms to search an element from a linear list implemented through static array, dynamic array and linked list. Int J Comput Appl 121(3):13–17

    Google Scholar 

  28. Shanker M, Hu MY, Hung MS (1996) Effect of data standardization on neural network training. Omega 24(4):385–397. https://doi.org/10.1016/0305-0483(96)00010-2

    Article  Google Scholar 

  29. Hagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Networks 5(6):989–993

    Article  CAS  Google Scholar 

  30. Lv C, Xing Y, Zhang J, Na X, Li Y, Liu T, Cao D, Wang F-Y (2017) Levenberg–Marquardt backpropagation training of multilayer neural networks for state estimation of a safety-critical cyber-physical system. IEEE Trans Industr Inf 14(8):3436–3446

    Article  Google Scholar 

  31. Garcia V, Debreuve E, Barlaud M (2008) Fast k nearest neighbor search using GPU. 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops. IEEE, Anchorage, pp 1–6. https://doi.org/10.1109/CVPRW.2008.4563100

    Chapter  Google Scholar 

  32. Dorf RC, Bishop RH (2000) Modern control systems. Prentice-Hall Inc., Upper Saddle River

    Google Scholar 

  33. Dawson CW, Wilby RL (2001) Hydrological modelling using artificial neural networks. Prog Phys Geogr Earth Environ 25(1):80–108. https://doi.org/10.1177/030913330102500104

    Article  Google Scholar 

  34. Lv C, Xing Y, Zhang J, Na X, Li Y, Liu T, Cao D, Wang F (2018) Levenberg–Marquardt backpropagation training of multilayer neural networks for state estimation of a safety-critical cyber-physical system. IEEE Trans Industr Inf 14(8):3436–3446. https://doi.org/10.1109/TII.2017.2777460

    Article  Google Scholar 

  35. DiPietro R, Hager GD (2020) Deep learning: RNNs and LSTM. In: Zhou SK, Rueckert D, Fichtinger G (eds) Handbook of medical image computing and computer assisted intervention. Academic Press, Cambridge, pp 503–519. https://doi.org/10.1016/B978-0-12-816176-0.00026-0

    Chapter  Google Scholar 

  36. Wirtz D, Karajan N, Haasdonk B (2015) Surrogate modeling of multiscale models using kernel methods. Int J Numer Meth Eng 101(1):1–28. https://doi.org/10.1002/nme.4767

    Article  Google Scholar 

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  1. School of Pharmacy, University of Otago, 18 Frederick St, North Dunedin, Dunedin, 9016, New Zealand

    Abdallah Derbalah, Hesham S. Al-Sallami & Stephen B. Duffull

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  1. Abdallah Derbalah
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  2. Hesham S. Al-Sallami
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  3. Stephen B. Duffull
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Derbalah, A., Al-Sallami, H.S. & Duffull, S.B. Reduction of quantitative systems pharmacology models using artificial neural networks. J Pharmacokinet Pharmacodyn 48, 509–523 (2021). https://doi.org/10.1007/s10928-021-09742-3

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  • DOI: https://doi.org/10.1007/s10928-021-09742-3

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