Cattani, Federica

Galvanin, Federico

Sangoi, Enrico

English

UCL Discovery

On the development and application of a general model identification framework to biological systemsEnrico Sangoi a, Federica Cattani b, Federico Galvanin a*a Department of Chemical Engineering, University College London, Torrington Place, London, WC1E 7JE, UKb Process Studies Group, Syngenta, Jealott's Hill International Research Centre, Berkshire, Bracknell, RG42 6EY, UK* Corresponding author: f.galvanin@ucl.ac.ukThe model building framework presented in the following diagram is based on well established approaches[1], but also employs a novel ANN-based model selection method[2] for model screening. The analyses conducted on the compartmental model showed that some parameters are unidentifiable, therefore it must be reformulated. Future works will include:• Reformulate non-identifiable models• Conduct identifiability analysis on physics-based mechanistic model• Test for distinguishability of the models• Proceed with model discrimination and model-based design of experimentsAcknowledgementThis project received funding from UCL Department of Chemical Engineering and Syngenta. The support is gratefully acknowledged.References:1. Franceschini, G., Macchietto, S., (2008). Model-based design of experiments for parameter precision: State of the art. Chemical Engineering Science, Model-Based Experimental Analysis 63, 4846–4872. 2. Quaglio, M., Roberts, L., Bin Jaapar, M.S., Fraga, E.S., Dua, V., Galvanin, F., (2020). An artificial neural network approach to recognise kinetic models from experimental data. Computers & Chemical Engineering 1353. Miao, H., Xia, X., Perelson, A.S., Wu, H., 2011. On identifiability of nonlinear ODE models and applications in viral dynamics. SIAM Rev Soc Ind Appl Math 53, 3–39.4. Wang, C.J., Liu, Z.Q., (2007). Foliar uptake of pesticides—Present status and future challenge. Pesticide Biochemistry and Physiology 87, 1–8.Mathematical modelling of biological systems has several challenges:• Partial understanding of the system• Limited observability• High uncertainty in the data (experimental error and intrinsic variability)• Trade-off between model complexity and interpretability• Time consuming and resource hungry experimentsProblemTackle these problems through a systematic model building strategy:• Tests to ensure the identifiability of the model parameters• Statistically-sound comparison of different models• Model-based design of experiments for better exploitation of resources • Quantification of the errors• Quantification of uncertainty on parameter estimates and model predictionsSolutionCompartmental modelMaterial  balance equations𝑑𝐶𝑖𝑑𝑡=෍𝑗(𝑘𝑗𝑖𝐶𝑗 − 𝑘𝑖𝑗𝐶𝑖)𝑚𝑖 = 𝐶𝑖𝑉𝑖State variables𝒙 ≔ {𝐶𝑖 , 𝑚𝑖}Observed statesෝ𝒚 : {𝑚𝑑𝑒𝑝𝑜𝑠𝑖𝑡 , 𝑚𝑐𝑢𝑡𝑖𝑐𝑙𝑒 , 𝑚𝑡𝑖𝑠𝑠𝑢𝑒 , 𝑚𝑟𝑜𝑝}Parameters𝜽 ≔ {𝑘𝑗𝑖 , 𝑉𝑖}a-posteriori practical identifiability testsMany phenomena involved in the foliar uptake of pesticides[4] :- Absorption - Diffusion- Equilibrium at interfaces- Metabolism- Volatility- PhotostabilityFoliar uptake of pesticidesIntroduction and MotivationMethodologyCase studyResults1. Models formulation2. Preliminary analysis of the models3. ANN-based first screening of the models4. Model discrimination + MD-MBDoE loop5. Parameter estimation + PP-MBDoE loopKey steps in the modelling procedurePersonal InformationProf. Federico GalvaninEnrico Sangoi Federica CattaniParameters correlation matrixRequires a preliminary estimation of the parameters (maximum likelihood estimate), it considers practical limitations on the data available.Results interpretation: highly correlated parameters are not practically identifiable, their effect cannot be decoupled with the I/O specified. Fisher Information Matrix𝑭𝑰𝑴 =෍𝑖=1𝑁𝜕 ො𝑦𝑖𝜕 መ𝜃𝑽−1𝜕 ො𝑦𝑖𝜕 መ𝜃Variance-Covariance matrix𝑽𝒂𝒓𝑪𝒐𝒗 = {𝐶𝑖𝑗} = 𝑭𝑰𝑴−1Correlation matrix𝑪𝒐𝒓𝒓 = 𝑟𝑖𝑗 ; 𝑟𝑖𝑗 =𝐶𝑖𝑗𝐶𝑖𝑖𝐶𝑗𝑗The following tests are considered to check identifiability conditions on the model parameters: a-priori structural identifiability and a-posteriori practical identifiability. [3]• Structural identifiability: differential algebra approach• Practical identifiability: correlation matrix and local sensitivity profilesPreliminary analysisFuture workActive ingredientAdjuvantLocal  sensitivity profilesThe profiles are obtained by manipulating one parameter at a time. Results interpretation: overlapping profiles lead to unidentifiable parameters. From the analysis it emerges which parts of the model should be modified to obtain an identifiable model. 

On the development and application of a general model identification framework to biological systems

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On the development and application of a general model identification framework to biological systems

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