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Bayesian Calibration for Modelling the Cardiovascular System Using the Two Element Windkessel Model
Get PDFDenne oppgaven utforsker egenskapene til Windkessel-modellene basert på syntetiske simuleringsstudier, og er en del av det tverrfaglige prosjektet "My Medical Digital Twin" ved NTNU. Windkessel-modellene estimerer de globale arterielle egenskapene ved å relatere målt (aorta) trykk og strømning gjennom lineære differensialligninger. Målet er å trekke slutninger om de fysisk tolkbare parameterne, nemlig total vaskulær motstand og arteriell elastisitet.
Inferens utføres ved å bruke en adaptiv MCMC-strategi. Dette lar oss utelate bruken av en emulator for data-modellen og er et av hovedbidragene til dette arbeidet. Som det andre hovedbidraget undersøker vi effekten av avhengig og uavhengig støy i simulerte trykkobservasjoner på usikkerheten og nøyaktigheten til parameterestimater. Dette er, så vidt vi vet, aldri gjort for Windkessel-modellene, og heller ikke for andre modeller basert på lineære differensialligninger.
En enkel simuleringsstudie bekrefter at det å ikke ta hensyn til modellavviket fører til uriktige og ustabile parameterestimater. Derfor er det inverse problemet satt i et Bayesiansk kalibreringsrammeverk, der avviket er modellert av en Gauss-prosess. Basert på syntetisk utledede trykkobservasjoner løses det inverse problemet ved å redegjøre for og kvantifisere usikkerheten i modellformuleringen og parameterestimatene.
Å estimere avviket lar oss gjenskape de sanne fysiske parameterne på en vellykket måte. Videre gir dette foreslåtte rammeverket en kjøretid for å estimere fysiske parametere for én persons trykk- og strømningsobservasjoner på bare sekunder. Vi demonstrerer også utfordringen med å inkorporere modellavvik i identifiserings-problemer med fysiske parametere. Dette løses gjennom informative priorer for observasjonsstøy og avviksparametere, som også gir de mest robuste parameterestimatene ved observasjoner med tidsavhengig støy.This thesis explores the properties of Windkessel Models based on synthetic simulation studies and is a part of the cross-disciplinary project "My Medical Digital Twin" at NTNU. The Windkessel models estimate the global arterial properties by relating measured (aortic) pressure and flow through linear differential equations. The aim is to make inferences about the physically interpretable parameters, namely, total vascular resistance and arterial compliance.
Inference is performed using an adaptive MCMC strategy. This allows us to successfully omit the use of an emulator for the computer model and is one of the main contributions of our work. As the second main contribution, we investigate the effect of dependent and independent noise in simulated pressure observations on the uncertainty and accuracy of parameter estimates. This is, to our knowledge, never done for the Windkessel models, nor other models based on linear differential equations.
We perform inference on models not accounting for the discrepancy, which confirms that not accounting for the model discrepancy leads to biased and unstable parameter estimates. Therefore, the inverse problem is set in a Bayesian calibration framework, where a Gaussian process models the discrepancy. Then, based on synthetically derived pressure observations, the inverse problem is solved, accounting for and quantifying the uncertainty in the model formulation and the parameter estimates.
Accounting for discrepancy allows us to recreate the true physical parameters successfully. Furthermore, this proposed framework yields a run time of estimating physical parameters for one person's pressure and flow observations to mere seconds. We also demonstrate the challenge of incorporating model discrepancy in confounding issues with physical parameters. This is solved through informative priors for observation noise and discrepancy parameters, yielding the most robust parameter estimates when subject to observations with time-dependent noise
Bayesian Calibration for Modelling the Cardiovascular System Using the Two Element Windkessel Model
No full textDenne oppgaven utforsker egenskapene til Windkessel-modellene basert på syntetiske simuleringsstudier, og er en del av det tverrfaglige prosjektet "My Medical Digital Twin" ved NTNU. Windkessel-modellene estimerer de globale arterielle egenskapene ved å relatere målt (aorta) trykk og strømning gjennom lineære differensialligninger. Målet er å trekke slutninger om de fysisk tolkbare parameterne, nemlig total vaskulær motstand og arteriell elastisitet.
Inferens utføres ved å bruke en adaptiv MCMC-strategi. Dette lar oss utelate bruken av en emulator for data-modellen og er et av hovedbidragene til dette arbeidet. Som det andre hovedbidraget undersøker vi effekten av avhengig og uavhengig støy i simulerte trykkobservasjoner på usikkerheten og nøyaktigheten til parameterestimater. Dette er, så vidt vi vet, aldri gjort for Windkessel-modellene, og heller ikke for andre modeller basert på lineære differensialligninger.
En enkel simuleringsstudie bekrefter at det å ikke ta hensyn til modellavviket fører til uriktige og ustabile parameterestimater. Derfor er det inverse problemet satt i et Bayesiansk kalibreringsrammeverk, der avviket er modellert av en Gauss-prosess. Basert på syntetisk utledede trykkobservasjoner løses det inverse problemet ved å redegjøre for og kvantifisere usikkerheten i modellformuleringen og parameterestimatene.
Å estimere avviket lar oss gjenskape de sanne fysiske parameterne på en vellykket måte. Videre gir dette foreslåtte rammeverket en kjøretid for å estimere fysiske parametere for én persons trykk- og strømningsobservasjoner på bare sekunder. Vi demonstrerer også utfordringen med å inkorporere modellavvik i identifiserings-problemer med fysiske parametere. Dette løses gjennom informative priorer for observasjonsstøy og avviksparametere, som også gir de mest robuste parameterestimatene ved observasjoner med tidsavhengig støy
Bayesian Calibration of Imperfect Computer Models using Physics-Informed Priors
Get PDFWe introduce a computational e_cient data-driven framework suitable for quantifying the uncertainty in physical parameters and model formulation of computer models, represented by di_erential equations. We construct physics-informed priors, which are multi-output GP priors that encode the model’s structure in the covariance function. This is extended into a fully Bayesian framework that quanti_es the uncertainty of physical parameters and model predictions. Since physical models often are imperfect descriptions of the real process, we allow the model to deviate from the observed data by considering a discrepancy function. For inference Hamiltonian Monte Carlo is used. Further, approximations for big data are developed that reduce the computational complexity from O(N3) to O(N _ m2); where m _ N: Our approach is demonstrated in simulation and real data case studies where the physics are described by time-dependent ODEs (cardiovascular models) and space-time dependent PDEs (heat equation). In the studies, it is shown that our modelling framework can recover the true parameters of the physical models in cases where 1) the reality is more complex than our modelling choice and 2) the data acquisition process is biased while also producing accurate predictions. Furthermore, it is demonstrated that our approach is computationally faster than traditional Bayesian calibration methods.publishedVersio
Bayesian Calibration of Imperfect Computer Models using Physics-Informed Priors
Get PDFWe introduce a computational efficient data-driven framework suitable for
quantifying the uncertainty in physical parameters and model formulation of
computer models, represented by differential equations. We construct
physics-informed priors, which are multi-output GP priors that encode the
model's structure in the covariance function. This is extended into a fully
Bayesian framework that quantifies the uncertainty of physical parameters and
model predictions. Since physical models often are imperfect descriptions of
the real process, we allow the model to deviate from the observed data by
considering a discrepancy function. For inference, Hamiltonian Monte Carlo is
used. Further, approximations for big data are developed that reduce the
computational complexity from to
where Our approach is demonstrated in simulation and real data case
studies where the physics are described by time-dependent ODEs describe
(cardiovascular models) and space-time dependent PDEs (heat equation). In the
studies, it is shown that our modelling framework can recover the true
parameters of the physical models in cases where 1) the reality is more complex
than our modelling choice and 2) the data acquisition process is biased while
also producing accurate predictions. Furthermore, it is demonstrated that our
approach is computationally faster than traditional Bayesian calibration
methods.Comment: 48 pages, 21 figure
Learning Physics between Digital Twins with Low-Fidelity Models and Physics-Informed Gaussian Processes
Get PDFA digital twin is a computer model that represents an individual, for
example, a component, a patient or a process. In many situations, we want to
gain knowledge about an individual from its data while incorporating imperfect
physical knowledge and also learn from data from other individuals. In this
paper, we introduce a fully Bayesian methodology for learning between digital
twins in a setting where the physical parameters of each individual are of
interest. A model discrepancy term is incorporated in the model formulation of
each personalized model to account for the missing physics of the low-fidelity
model. To allow sharing of information between individuals, we introduce a
Bayesian Hierarchical modelling framework where the individual models are
connected through a new level in the hierarchy. Our methodology is demonstrated
in two case studies, a toy example previously used in the literature extended
to more individuals and a cardiovascular model relevant for the treatment of
Hypertension. The case studies show that 1) models not accounting for imperfect
physical models are biased and over-confident, 2) the models accounting for
imperfect physical models are more uncertain but cover the truth, 3) the models
learning between digital twins have less uncertainty than the corresponding
independent individual models, but are not over-confident.Comment: 33 pages, 19 figure
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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