On Computational Modeling of Biological Development

Teemu J. Häkkinen

Biologisen kehityksen laskennallisesta mallintamisesta

Teemu J. Häkkinen

Matematiikan ja systeemianalyysin laitos

Tutkimustuotos: Doctoral Thesis › Collection of Articles

Abstrakti

Tässä väitöskirjassa tarkastellaan biologisen kaavoituksen ja kasvun matemaattista mallinnusta. Perimmäisenä tavoitteena on rakentaa realistisia mutta tehokkaita matemaattisia malleja kuvaamaan sekä biologisten rakenteiden muodostumista että laajemmin evolutiivisia prosesseja, jotka muovaavat noita rakenteita. Kehitykselliset mekanismit sekä ohjaavat että rajoittavat biologisten rakenteiden evoluutiota, ja matemaattiset mallit tarjoavat tehokkaan työkalun noiden rajoitusten ymmärtämiseen. Ensimmäisessä tutkimuksessa tarkastellaan nisäkäshampaiden evolutiivisten muutoksien kehitysmekanismeja. Hiiren hampaan kehitystä muunnellaan kokeellisesti, ja tuloksena pystytään tuottamaan tasaisia siirtymiä eri muotojen välillä. Kokeelliset tulokset pystytään toistamaan uskottavasti hampaan kehitystä kuvaavan tietokonemallin avulla. Tietokonemalli on toteutettu käyttäjäystävälliseen käyttöliittymään, tavoitteena helpottaa poikkitieteellistä yhteistyötä biologien ja matemaatikkojen välillä. Toisessa tutkimuksessa tarkastellaan hiiren kielen makunystyjen koon ja etäisyyden välistä yhteyttä. Kokeissa havaitaan, että muuntelemalla FGF-signalointia systeemissä nystyjen koko muuttuu keskimääräisen etäisyyden säilyessä vakiona. Tulosten perusteella ehdotetaan, että FGF-signaali vaikuttaa Wnt-signaalin toimintaan muuttamalla Wnt:n paikallista diffuusiota geenitranskription sijaan. Hypoteesille saadaan tukea tietokonemallista, jossa klassista reaktio-diffuusio (Turing) mallia laajennetaan korvaamalla diffuusiovakio epälineaarisella funktiolla. Kolmannessa tutkimuksessa esitetään hampaan kiilteen muodostumiselle matemaattinen malli, jossa kiilteen muodostumisen oletetaan olevan ravinnediffuusiorajoitteinen ilmiö. Tutkimuksessa osoitetaan, että malli kykenee toistamaan paksun kiilteen päällä esiintyvät rakennemuodot lähtien liikkeelle kiilteen alla olevista hampaan rakenteista. Neljännessä tutkimuksessa tarkastellaan Stokesin yhtälön soveltamista kudoksen kasvun mallintamiseen. Stokesin yhtälöstä käytetään laajempaa muotoa, jossa huomioidaan vaihteleva viskositeetti ja massalähteet. Systeemiin liitetään reaktio-diffuusio kaavoitusmekanismi, joka on laajennettu solujen erikoistumista kuvaavalla mekanismilla. Tutkimuksessa kehitetään tehokas numeerinen alusta ongelman ratkaisemiseksi, jonka tarkkuutta tutkitaan numeerisilla testeillä joiden ratkaisu tunnetaan. Mallin toimintaa esitellään kuvaamalla ideaalin kudoksen kasvua tilanteissa, joissa on vaihteleva pintajännite ja erilaisia viskositeettiprofiileja.

Julkaisun otsikon käännös	Biologisen kehityksen laskennallisesta mallintamisesta
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Valvoja/neuvonantaja	Hannukainen, Antti, Vastuuprofessori Jernvall, Jukka, Ohjaaja
Kustantaja	Aalto University
Painoksen ISBN	978-952-60-8725-2
Sähköinen ISBN	978-952-60-8726-9
Tila	Julkaistu - 2019
OKM-julkaisutyyppi	G5 Tohtorinväitöskirja (artikkeli)

Tutkimusalat

elementtimenetelmä
level set -menetelmä
Stokesin yhtälö
diffuusiorajoitteinen kasvu
vapaan reunan ongelma
kudoksen kasvu
laskennallinen mallintaminen
morfogeneesi

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-60-8726-9

Sormenjälki Sukella tutkimusaiheisiin 'Biologisen kehityksen laskennallisesta mallintamisesta'. Ne muodostavat yhdessä ainutlaatuisen sormenjäljen.

Siteeraa tätä

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title = "On Computational Modeling of Biological Development",

abstract = "This thesis considers the mathematical modeling of patterning and growth in biological systems. The fundamental objective is to build realistic, yet efficient and well-described mathematical models of morphogenesis to help understand not just the specific systems under study, but ultimately the evolutionary processes that sculpt the biological forms, from tissues to complete organs. Developmental mechanisms both guide and restrict the evolution of biological forms, and mathematical models provide a powerful tool to understand the role and significance of those restrictions. The first study considers the developmental mechanisms of evolutionary transitions in mammalian dentition. In the study, the development of mouse molars is experimentally controlled, and a smooth transition in tooth morphology is demonstrated in response to controlling a single signaling morphogen. The experimental results are plausibly recapitulated in a computational model of tooth development, which is implemented in a user-friendly interface with the aim of bridging the traditional gap between biologists doing the experiments and mathematicians building the models. The second study investigates the relation between size and spacing of the taste papillae in the mouse tongue. It is observed that experimentally controlling the FGF signaling changes the size but not the spacing of the taste papillae. Based on the results it is suggested that FGF signaling affects the extend of canonical Wnt signaling by changing the local diffusion of Wnt. Support for the hypothesis is obtained from simulations of a reaction-diffusion (Turing) model, where the activator morphogen diffusion constant is replaced with a non-linear function. In the third study, a mathematical model of tooth enamel formation is proposed. The model assumes that the process of laying down the enamel in teeth is limited by the diffusion of nutrients required by the secreting cells. Using computer simulations it is demonstrated how the model is capable of plausibly reproducing the enamel surface patterns on the top of thick enamel, resulting from the uneven surface of the underlying tooth structures. The fourth study considers the application of the Stokes equation for the simulation of tissue growth. The system is coupled with a reaction-diffusion system augmented with a differentiation mechanism to mimic the state-changes in cells, such as the establishment of signaling centers. An efficient numerical framework for solving the system in 3D is developed, and the implementation is validated using numerical tests with known solutions. To demonstrate the model dynamics, idealized tissue growth is simulated in scenarios with varying amounts of surface tension and incorporating non-homogeneous viscosity profiles.",

keywords = "finite element method, level set method, Stokes equation, diffusion-limited growth, free boundary problems, tissue growth, computational modeling, morphogenesis, elementtimenetelm{\"a}, level set -menetelm{\"a}, Stokesin yht{\"a}l{\"o}, diffuusiorajoitteinen kasvu, vapaan reunan ongelma, kudoksen kasvu, laskennallinen mallintaminen, morfogeneesi, finite element method, level set method, Stokes equation, diffusion-limited growth, free boundary problems, tissue growth, computational modeling, morphogenesis",

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AU - Häkkinen, Teemu J.

PY - 2019

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N2 - This thesis considers the mathematical modeling of patterning and growth in biological systems. The fundamental objective is to build realistic, yet efficient and well-described mathematical models of morphogenesis to help understand not just the specific systems under study, but ultimately the evolutionary processes that sculpt the biological forms, from tissues to complete organs. Developmental mechanisms both guide and restrict the evolution of biological forms, and mathematical models provide a powerful tool to understand the role and significance of those restrictions. The first study considers the developmental mechanisms of evolutionary transitions in mammalian dentition. In the study, the development of mouse molars is experimentally controlled, and a smooth transition in tooth morphology is demonstrated in response to controlling a single signaling morphogen. The experimental results are plausibly recapitulated in a computational model of tooth development, which is implemented in a user-friendly interface with the aim of bridging the traditional gap between biologists doing the experiments and mathematicians building the models. The second study investigates the relation between size and spacing of the taste papillae in the mouse tongue. It is observed that experimentally controlling the FGF signaling changes the size but not the spacing of the taste papillae. Based on the results it is suggested that FGF signaling affects the extend of canonical Wnt signaling by changing the local diffusion of Wnt. Support for the hypothesis is obtained from simulations of a reaction-diffusion (Turing) model, where the activator morphogen diffusion constant is replaced with a non-linear function. In the third study, a mathematical model of tooth enamel formation is proposed. The model assumes that the process of laying down the enamel in teeth is limited by the diffusion of nutrients required by the secreting cells. Using computer simulations it is demonstrated how the model is capable of plausibly reproducing the enamel surface patterns on the top of thick enamel, resulting from the uneven surface of the underlying tooth structures. The fourth study considers the application of the Stokes equation for the simulation of tissue growth. The system is coupled with a reaction-diffusion system augmented with a differentiation mechanism to mimic the state-changes in cells, such as the establishment of signaling centers. An efficient numerical framework for solving the system in 3D is developed, and the implementation is validated using numerical tests with known solutions. To demonstrate the model dynamics, idealized tissue growth is simulated in scenarios with varying amounts of surface tension and incorporating non-homogeneous viscosity profiles.

AB - This thesis considers the mathematical modeling of patterning and growth in biological systems. The fundamental objective is to build realistic, yet efficient and well-described mathematical models of morphogenesis to help understand not just the specific systems under study, but ultimately the evolutionary processes that sculpt the biological forms, from tissues to complete organs. Developmental mechanisms both guide and restrict the evolution of biological forms, and mathematical models provide a powerful tool to understand the role and significance of those restrictions. The first study considers the developmental mechanisms of evolutionary transitions in mammalian dentition. In the study, the development of mouse molars is experimentally controlled, and a smooth transition in tooth morphology is demonstrated in response to controlling a single signaling morphogen. The experimental results are plausibly recapitulated in a computational model of tooth development, which is implemented in a user-friendly interface with the aim of bridging the traditional gap between biologists doing the experiments and mathematicians building the models. The second study investigates the relation between size and spacing of the taste papillae in the mouse tongue. It is observed that experimentally controlling the FGF signaling changes the size but not the spacing of the taste papillae. Based on the results it is suggested that FGF signaling affects the extend of canonical Wnt signaling by changing the local diffusion of Wnt. Support for the hypothesis is obtained from simulations of a reaction-diffusion (Turing) model, where the activator morphogen diffusion constant is replaced with a non-linear function. In the third study, a mathematical model of tooth enamel formation is proposed. The model assumes that the process of laying down the enamel in teeth is limited by the diffusion of nutrients required by the secreting cells. Using computer simulations it is demonstrated how the model is capable of plausibly reproducing the enamel surface patterns on the top of thick enamel, resulting from the uneven surface of the underlying tooth structures. The fourth study considers the application of the Stokes equation for the simulation of tissue growth. The system is coupled with a reaction-diffusion system augmented with a differentiation mechanism to mimic the state-changes in cells, such as the establishment of signaling centers. An efficient numerical framework for solving the system in 3D is developed, and the implementation is validated using numerical tests with known solutions. To demonstrate the model dynamics, idealized tissue growth is simulated in scenarios with varying amounts of surface tension and incorporating non-homogeneous viscosity profiles.

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KW - level set -menetelmä

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KW - vapaan reunan ongelma

KW - kudoksen kasvu

KW - laskennallinen mallintaminen

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KW - level set method

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KW - free boundary problems

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