Inference of Nonlinear State-Space Models for Sandwich-Type Lateral Flow Immunoassay Using Extended Kalman Filtering

In this paper, a mathematical model for sandwich-type lateral flow immunoassay is developed via short available time series. A nonlinear dynamic stochastic model is considered that consists of the biochemical reaction system equations and the observation equation. After specifying the model structure, we apply the extended Kalman filter (EKF) algorithm for identifying both the states and parameters of the nonlinear state-space model. It is shown that the EKF algorithm can accurately identify the parameters and also predict the system states in the nonlinear dynamic stochastic model through an iterative procedure by using a small number of observations. The identified mathematical model provides a powerful tool for testing the system hypotheses and also for inspecting the effects from various design parameters in both rapid and inexpensive way. Furthermore, by means of the established model, the dynamic changes in the concentration of antigens and antibodies can be predicted, thereby making it possible for us to analyze, optimize, and design the properties of lateral flow immunoassay devices.

[1]  Xiao-Li Hu,et al.  A Basic Convergence Result for Particle Filtering , 2008, IEEE Transactions on Signal Processing.

[2]  Gregory T. A. Kovacs,et al.  Optical Scanner for Immunoassays With Up-Converting Phosphorescent Labels , 2008, IEEE Transactions on Biomedical Engineering.

[3]  Huijun Gao,et al.  A Parameter-Dependent Approach to Robust $H_{\infty }$ Filtering for Time-Delay Systems , 2008, IEEE Transactions on Automatic Control.

[4]  Alex Simpkins,et al.  System Identification: Theory for the User, 2nd Edition (Ljung, L.; 1999) [On the Shelf] , 2012, IEEE Robotics & Automation Magazine.

[5]  Huijun Gao,et al.  A new design of robust H2 filters for uncertain systems , 2008, Syst. Control. Lett..

[6]  Gamini Dissanayake,et al.  Convergence and Consistency Analysis for Extended Kalman Filter Based SLAM , 2007, IEEE Transactions on Robotics.

[7]  Raphael C. Wong,et al.  Lateral flow immunoassay , 2009 .

[8]  Jim Carney,et al.  Rapid, Sensitive, and Specific Lateral-Flow Immunochromatographic Point-of-Care Device for Detection of Herpes Simplex Virus Type 2-Specific Immunoglobulin G Antibodies in Serum and Whole Blood , 2007, Clinical and Vaccine Immunology.

[9]  Gallya Gannot,et al.  Molecular Profiling of Cancer , 2004, Toxicologic pathology.

[10]  Yeun-Chung Lee,et al.  One-step immunochromatographic assay for the detection of Staphylococcus aureus , 2007 .

[11]  Steven X. Ding,et al.  State and Disturbance Estimator for Time-Delay Systems With Application to Fault Estimation and Signal Compensation , 2007, IEEE Transactions on Signal Processing.

[12]  C Dok An,et al.  Evaluation of a rapid qualitative prostate specific antigen assay, the One Step PSA(TM) test. , 2001, Cancer letters.

[13]  Shizhi Qian,et al.  A mathematical model of lateral flow bioreactions applied to sandwich assays. , 2003, Analytical biochemistry.

[14]  M. Xiong,et al.  Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks , 2008, PloS one.

[15]  A. Corigliano,et al.  Parameter identification in explicit structural dynamics: performance of the extended Kalman filter , 2004 .

[16]  Liberty Sibanda,et al.  Development of a colloidal gold-based lateral-flow immunoassay for the rapid simultaneous detection of zearalenone and deoxynivalenol , 2007, Analytical and bioanalytical chemistry.

[17]  A. Krener.  The Convergence of the Extended Kalman Filter , 2002, math/0212255.

[18]  Huijie Huang,et al.  Research of reflectance photometer based on optical absorption , 2010 .

[19]  Yurong Li,et al.  Study on the Methodology of Quantitative Gold Immunochromatographic Strip Assay , 2010, 2010 2nd International Workshop on Intelligent Systems and Applications.

[20]  Shiang-Bin Jong,et al.  Rapid and simple quantitative measurement of alpha-fetoprotein by combining immunochromatographic strip test and artificial neural network image analysis system. , 2004, Clinica chimica acta; international journal of clinical chemistry.

[21]  Nicolas Brunel,et al.  Estimating parameters and hidden variables in non-linear state-space models based on ODEs for biological networks inference , 2007, Bioinform..

[22]  Prem K. Goel,et al.  Bayesian estimation via sequential Monte Carlo sampling - Constrained dynamic systems , 2007, Autom..

[23]  A. H. Mohamed,et al.  Adaptive Kalman Filtering for INS/GPS , 1999 .

[24]  Grish C Varshney,et al.  Immunochromatographic dipstick assay format using gold nanoparticles labeled protein-hapten conjugate for the detection of atrazine. , 2007, Environmental science & technology.

[25]  Guohua Cheng,et al.  Development of an immunochromatographic assay for the rapid detection of bromoxynil in water. , 2008, Environmental pollution.

[26]  Fuwen Yang,et al.  Stochastic Dynamic Modeling of Short Gene Expression Time-Series Data , 2008, IEEE Transactions on NanoBioscience.

[27]  Zidong Wang,et al.  An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series , 2009, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[28]  Hong Yang,et al.  A sensitive immunochromatographic assay using colloidal gold-antibody probe for rapid detection of pharmaceutical indomethacin in water samples. , 2009, Biosensors & bioelectronics.

[29]  Gaiping Zhang,et al.  Development of a lateral flow immunoassay strip for screening of sulfamonomethoxine residues , 2008, Food additives & contaminants. Part A, Chemistry, analysis, control, exposure & risk assessment.

[30]  B. Palsson,et al.  Formulating genome-scale kinetic models in the post-genome era , 2008, Molecular systems biology.

[31]  Ying Zong,et al.  Development of An Immunochromatographic Assay System for the Quantitative Determination of Alpha-fetoprotein , 2003 .

[32]  Tatsuro Endo,et al.  A novel enhancement assay for immunochromatographic test strips using gold nanoparticles , 2006, Analytical and bioanalytical chemistry.

[33]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[34]  Shizhi Qian,et al.  Analysis of lateral flow biodetectors: competitive format. , 2004, Analytical biochemistry.