Generalized sensitivity functions for multiple output systems

Kappel, Franz; Munir, Mohammad

doi:10.1515/jiip-2016-0024

Cited by 11 publications

(7 citation statements)

References 11 publications

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“…These results suggest that the available data do not support the complexity of the model. A future study may apply a systematic analysis of model sensitivity and parameter correlations, for example using the profile-likelihood method of Raue et al (35) or generalized sensitivity functions of Thomaseth and Cobelli (36) [extended to multiple output models by Kappel and Munir (37)]. Another potential study for future work could involve estimating model parameters from synthetic timecourse data, to see whether more frequent sampling or a longer observation period provides more stable parameter estimates.…”

Section: Discussionmentioning

confidence: 99%

Parameter Identification for a Model of Neonatal Fc Receptor-Mediated Recycling of Endogenous Immunoglobulin G in Humans

Kendrick

Evans

Berlanga³

et al. 2019

Front. Immunol.

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Salvage of endogenous immunoglobulin G (IgG) by the neonatal Fc receptor (FcRn) is implicated in many clinical areas, including therapeutic monoclonal antibody kinetics, patient monitoring in IgG multiple myeloma, and antibody-mediated transplant rejection. There is a clear clinical need for a fully parameterized model of FcRn-mediated recycling of endogenous IgG to allow for predictive modeling, with the potential for optimizing therapeutic regimens for better patient outcomes. In this paper we study a mechanism-based model incorporating nonlinear FcRn-IgG binding kinetics. The aim of this study is to determine whether parameter values can be estimated using the limited in vivo human data, available in the literature, from studies of the kinetics of radiolabeled IgG in humans. We derive mathematical descriptions of the experimental observations—timecourse data and fractional catabolic rate (FCR) data—based on the underlying physiological model. Structural identifiability analyses are performed to determine which, if any, of the parameters are unique with respect to the observations. Structurally identifiable parameters are then estimated from the data. It is found that parameter values estimated from timecourse data are not robust, suggesting that the model complexity is not supported by the available data. Based upon the structural identifiability analyses, a new expression for the FCR is derived. This expression is fitted to the FCR data to estimate unknown parameter values. Using these parameter estimates, the plasma IgG response is simulated under clinical conditions. Finally a suggestion is made for a reduced-order model based upon the newly derived expression for the FCR. The reduced-order model is used to predict the plasma IgG response, which is compared with the original four-compartment model, showing good agreement. This paper shows how techniques for compartmental model analysis—structural identifiability analysis, linearization, and reparameterization—can be used to ensure robust parameter identification.

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Section: Discussionmentioning

confidence: 99%

Parameter Identification for a Model of Neonatal Fc Receptor-Mediated Recycling of Endogenous Immunoglobulin G in Humans

Kendrick

Evans

Berlanga³

et al. 2019

Front. Immunol.

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“…In this chapter, we analyze the proposed model of vascular refilling with inflammation presented in the previous chapter. We apply sensitivity analysis, parameter estimation, and subset selection methods as discussed in the papers [86,87,88,89]. Measurements for at least one output of the system are essential in our analyses.…”

Section: Analysis and Discussionmentioning

confidence: 99%

“…The following sections discuss theories on sensitivity analysis, subset selection, and parameter estimation using [86,87,88,89] as main references. We then apply these methods on the proposed model with hematocrit and fluid flux as model outputs, and with respect to the parameters a, L, d, b and c. Two cases are considered in the estimation of parameters: first, when CRP concentration is slightly elevated and second, when CRP concentration is high.…”

Section: Analysis and Discussionmentioning

confidence: 99%

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A model of vascular refilling with inflammation

Paguio

Kappel

Kotanko

2018

Mathematical Biosciences

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Inflammation is prevalent in hemodialysis patients and is believed to significantly contribute to cardiovascular disease progression in end stage renal disease patients undergoing hemodialysis. Increased vascular permeability associated with inflammation is likely to influence the capillary wall properties, affecting vascular refilling during hemodialysis. In this paper, we present a model that incorporates inflammation into a vascular refilling model. We investigate how inflammation may affect the fluid volume and protein concentration dynamics in the plasma and interstitial spaces. In our work, we quantify inflammation by considering the concentration of the inflammatory biomarker C-reactive protein (CRP). Traditional sensitivity functions and subset selection based on asymptotic standard errors were used to aid in parameter identification. Estimates of the parameters were calculated from numerically generated measurements for fluid flux and hematocrit. Observations on the capillary wall properties, filtration and reflection coefficients, were done using data on mean CRP and serum albumin from a large population of European hemodialysis patients in their terminal two years before death and patients surviving for at least four years after dialysis initiation.

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“…Since novel model is a compartmental model with six outputs G p , G i , Q 1a , Q 1b and Q 2 , we consider a multiple-output system with the measurable outputs [8], [14] modeled by…”

Section: Sensitivity Analysismentioning

confidence: 99%

A Polynomial Linear Regression Approach to Estimate Sensitive Parameters in the Novel Double Diabetes Model

Hussain

Arbab

Salahuddin

et al. 2020

ijaa

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Sensitivity analysis characterizes the changes in the model outputs due to the changes in the model parameters. In this article, we estimate the most sensitive parameters in the Novel Double Diabetes Model (NDDM) through the polynomial linear regression approach; this way we develop a direct relation between the sensitivity analysis and the paramter estimation. The NDDM has more than seventeen parameters, and estimating them simultanously is difficult. We select the most commonly used five parameters in the glucose-insulin dynamics for the sensitivity analysis. The model outputs-glucose concentrations in the plasma and the subcutaneous compartments are sensitive to the selected parameters whereas the insulin concentrations in the plasma and the subcutaneous compartment are sensitive only to the insulin transfer rate from the subcutaneous to the plasma compartment. System sensitivity of the model for the selected parameters is also in agreement with the individual sensitivities of the parameters. Consequently, we estimate the parameters which are more sensitive by the polynomial linear regression approach.

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Generalized sensitivity functions for multiple output systems

Cited by 11 publications

References 11 publications

Parameter Identification for a Model of Neonatal Fc Receptor-Mediated Recycling of Endogenous Immunoglobulin G in Humans

Parameter Identification for a Model of Neonatal Fc Receptor-Mediated Recycling of Endogenous Immunoglobulin G in Humans

A model of vascular refilling with inflammation

A Polynomial Linear Regression Approach to Estimate Sensitive Parameters in the Novel Double Diabetes Model

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