Multivariat analyse som verktøy til forståelse og reduksjon av kompleksitet av matematiske modeller i systembiologi

In the area of systems biology, technologies develop very fast, which allows us to collect massive amounts of various data. The main interest of scientists is to receive an insight into the obtained data sets and discover their inherent properties. Since the data often are rather complex and intimidating equations may be required for modelling, data analysis can be quite challenging for the majority of bio-scientists who do not master advanced mathematics. In this thesis it is proposed to use multivariate statistical methods as a tool for understanding the properties of complex models used for describing biological systems. The methods of multivariate analysis employed in this thesis search for latent variables that form a basis of all processes in a system. This often reduces dimensions of the system and makes it easier to get the whole picture of what is going on. Thus, in this work, methods of multivariate analysis were used with a descriptive purpose in Papers I and IV to discover effects of input variables on a response. Often it is necessary to know a functional form that could have generated the collected data in order to study the behaviour of the system when one or another parameter is tuned. For this purpose, we propose the Direct Look-Up (DLU) approach that is claimed here to be a worthy alternative to the already existing fitting methods due to its high computational speed and ability to avoid many problems such as subjectivity, choice of initial values, local optima and so on (Papers II and III). Another aspect covered in this thesis is an interpretation of function parameters by the custom human language with the use of multivariate analysis. This would enable mathematicians and bio-scientists to understand each other when describing the same object. It was accomplished here by using the concept of a metamodel and sensory analysis in Paper IV. In Paper I, a similar approach was used even though the main focus of the paper was slightly different. The original aim of the article was to show the advantages of the multi-way GEMANOVA analysis over the traditional ANOVA analysis for certain types of data. However, in addition, the relationship between human profiling of data samples and function parameters was discovered. In situations when funds for conducting experiments are limited and it is unrealizable to study all possible parameter combinations, it is necessary to have a smart way of choosing a few but most representative conditions for a particular system. In Paper V Multi-level Binary Replacement design (MBR) was developed as such, which can also be used for searching for a relevant parameter range. This new design method was applied here in Papers II and IV for selection of samples for further analyses.Teknologiutviklingen innenfor systembiologien er nå så rask at det gir mulighet til å samle svært store datamengder på kort tid og til relativ lav pris. Hovedinteressen til forskerne er typisk å få innsikt i dataene og deres iboende egenskaper. Siden data kan være ganske komplekse og ofte beskrives ved kompliserte, gjerne ikke-lineære, funksjoner, kan dataanalyse være ganske utfordrende for mange bioforskere som ikke behersker avansert matematikk. I dette arbeidet er det foreslått å bruke multivariat statistisk analyse for å komme nærmere en forståelse av egenskapene av kompliserte modeller som blir brukt for å beskrive biologiske systemer. De multivariate metodene som er benyttet i denne avhandlingen søker etter latente variabler som utgjør en lineær basis og tilnærming til de komplekse prosessene i et system. Dermed kan man oppnå en forenkling av systemet som er lettere å tolke. I dette arbeidet ble multivariate analysemetoder brukt i denne beskrivende hensikten i Artikler (Papers) I og IV til å oppdage effekter av funksjonsparametre på egenskapene til komplekse matematiske modeller. Ofte er det nødvendig å finne en matematisk funksjon som kunne ha generert de innsamlede dataene for å studere oppførselen av systemet. Med den hensikt foreslår vi en metode for modelltilpasning ved DLU-metoden (the Direct Look-Up) som her påstås å være et verdifullt alternativ til de eksisterende estimeringsmetodene på grunn av høy fart og evne til å unngå typiske problemer som for eksempel subjektivitet, valg av initialverdier, lokale optima, m.m (Artikler II og III). Et annet aspekt dekket i denne avhandlingen er bruken av multivariat analyse til å gi tolking av matematiske funksjonsparametre ved hjelp av et dagligdags vokabular. Dette kan gjøre det enklere for matematikere og bioforskere å forstå hverandre når de beskriver det samme objektet. Det var utført her ved å benytte ideen om en metamodell og sensorisk analyse i Artikkel IV. I Artikkel I var en lignende metode også brukt for å få sensoriske beskrivelser av bilder generert fra differensiallikninger. Hovedfokuset i Artikkel I var imidlertid et annet, nemlig å vise fordelen ved multi-way GEMANOVA-analyse fremfor den tradisjonelle ANOVA-analysen for visse datatyper. I denne artikkelen ble GEMANOVA brukt til å avdekke sammenhengen mellom kompliserte kombinasjoner av funksjonsparametrene og bildedeskriptorer. I situasjoner der ressurser til å utføre eksperimenter er begrenset og det er umulig å prøve ut alle kombinasjoner av parametre, er det behov for metoder som kan bestemme et fåtall av parameterinnstillinger som er mest mulig representative for et bestemt system. I Artikkel V ble derfor Multi-level Binary Replacement (MBR) design utviklet som en sådan, og den kan også brukes for å søke etter et relevant parameterrom for datasimuleringer. Den nye designmetoden ble anvendt i Artikler II og IV for utvelgelse av parameterverdier for videre analyser

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Half of the patients suffering from atrial fibrillation (AF) cannot be treated adequately, today. This thesis presents multi-scale computational methods to advance our understanding of patho-mechanisms, to improve the diagnosis of patients harboring an arrhythmogenic substrate, and to tailor therapy. The modeling pipeline ranges from ion channels on the subcellular level up to the ECG on the body surface. The tailored therapeutic approaches carry the potential to reduce the burden of AF

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Half of the patients suffering from atrial fibrillation (AF) cannot be treated adequately, today. This book presents multi-scale computational methods to advance our understanding of patho-mechanisms, to improve the diagnosis of patients harboring an arrhythmogenic substrate, and to tailor therapy. The modeling pipeline ranges from ion channels on the subcellular level up to the ECG on the body surface. The tailored therapeutic approaches carry the potential to reduce the burden of AF

Modeling Human Atrial Patho-Electrophysiology from Ion Channels to ECG - Substrates, Pharmacology, Vulnerability, and P-Waves

Half of the patients suffering from atrial fibrillation (AF) cannot be treated adequately, today. This book presents multi-scale computational methods to advance our understanding of patho-mechanisms, to improve the diagnosis of patients harboring an arrhythmogenic substrate, and to tailor therapy. The modeling pipeline ranges from ion channels on the subcellular level up to the ECG on the body surface. The tailored therapeutic approaches carry the potential to reduce the burden of AF