Parameter estimation of systems with delays via structural sensitivity analysis

Fujarewicz, Krzysztof; Łakomiec, Krzysztof

doi:10.3934/dcdsb.2014.19.2521

Cited by 10 publications

(5 citation statements)

References 18 publications

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“…Bars appearing in these figures indicate variations of corresponding signals or sensitivity models of corresponding subsystems. A more detailed description of all the structural transformations used in this paper can be found in a previous study …”

Section: Problem Solutionmentioning

confidence: 99%

“…In contrast to classical cellular automaton which are systems "purely discrete" (time, space, and state are described by discrete values), a coupled map lattice operates on continuous states of cells (space and time remain discrete). We use in this work structural adjoint sensitivity analysis, which is a special method that utilizes the adjoint system constructed by particular transformation of the analysed model given in a block‐diagram form . This method is useful in analyzing Multiple‐Input Single‐Output (MISO) systems due to the low computational complexity for these systems.…”

Section: Introductionmentioning

confidence: 99%

“…For example, adjoint sensitivity analysis is useful in a parameter estimation process where the analyzed system has many inputs (parameters) and usually one scalar output describing the system (objective function). In a previous study, this method is used to estimate parameters of various types of mathematical models. In the present work, structural adjoint sensitivity analysis is used to compute the spatiotemporal gradient of the objective function with respect to the input signal which affects the system of a 1D cellular automaton with a continuous state.…”

Section: Introductionmentioning

confidence: 99%

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Spatiotemporal sensitivity of systems modeled by cellular automata

Fujarewicz

Łakomiec

2018

Math Methods in App Sciences

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Cellular automata are frequently used to model dynamics of spatial systems.This work shows how a so-called structural adjoint sensitivity analysis may be applied to such systems. It is assumed that the cellular automaton has a continuous state, a spatiotemporal input, and is characterized by one scalar objective function specified, for example, in a given optimization or parameter optimization problem. With this analysis, it is possible to calculate efficiently a gradient of the objective function in a space of the spatiotemporal input of the automata.As an example, a model of tumor growth with an introduced spatiotemporal irradiation signal is analysed.

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Section: Problem Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spatiotemporal sensitivity of systems modeled by cellular automata

Fujarewicz

Łakomiec

2018

Math Methods in App Sciences

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“…In this work we use adjoint sensitivity analysis, which is a sensitivity method that utilizes the adjoint system constructed based on the analyzed model and simulated backward in time. Adjoint sensitivity analysis, in a special structural form, is especially useful for models described by block diagrams and was originally developed for neural networks [2] and afterwards was used for different models described by ordinary differential equations [3,4,8,9], systems with delays [5] and agestructured models [7]. Adjoint sensitivity analysis is especially useful in analyzing MISO (Multiple-Input Single-Output) systems due to the much lower computational complexity when compared to forward sensitivity analysis.…”

Section: Krzysztof Fujarewicz and Krzysztof Lakomiecmentioning

confidence: 99%

Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization

Fujarewicz¹,

Łakomiec²

2016

MBE

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We investigate a spatial model of growth of a tumor and its sensitivity to radiotherapy. It is assumed that the radiation dose may vary in time and space, like in intensity modulated radiotherapy (IMRT). The change of the final state of the tumor depends on local differences in the radiation dose and varies with the time and the place of these local changes. This leads to the concept of a tumor's spatiotemporal sensitivity to radiation, which is a function of time and space. We show how adjoint sensitivity analysis may be applied to calculate the spatiotemporal sensitivity of the finite difference scheme resulting from the partial differential equation describing the tumor growth. We demonstrate results of this approach to the tumor proliferation, invasion and response to radiotherapy (PIRT) model and we compare the accuracy and the computational effort of the method to the simple forward finite difference sensitivity analysis. Furthermore, we use the spatiotemporal sensitivity during the gradient-based optimization of the spatiotemporal radiation protocol and present results for different parameters of the model.

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“…Sensitivity analysis can be viewed as study of how the change of system’s input affects the change of particular system’s output. This kind of analysis has been used in our previous works to study the behaviour of complex biomedical models [5], parameter estimation process of mathematical models described by various type of differential equations [6–9], or during control optimization tasks [10, 11].…”

Section: Introductionmentioning

confidence: 99%

Time-dependent synergy for multi-agent anticancer therapy

Fujarewicz

Łakomiec

2020

Preprint

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A synergy between two therapeutic agents occurs when the effect of using both is greater than the sum of the effects of using each of them separately. There are several methods of detecting synergies in the literature, but they do not take into account the relationship between the times in which the factors act. In the article, we propose and justify the use of second-order sensitivity analysis as a potential tool for the detection and visualization of this type of synergy. We test and illustrate the proposed approach using four exemplary models of combined radio-chemotherapy of cancer.

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Parameter estimation of systems with delays via structural sensitivity analysis

Cited by 10 publications

References 18 publications

Spatiotemporal sensitivity of systems modeled by cellular automata

Spatiotemporal sensitivity of systems modeled by cellular automata

Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization

Time-dependent synergy for multi-agent anticancer therapy

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